Melty Blood/WMG

The goofy parts of the game slip into The Dreaming.
As per the original Changeling: The Dreaming with a dash of Neil Gaiman. Neco Arc, Neco Arc Chaos and G. Akiha are dream spirits ("Chimera") and the maids, Miyako and Satsuki are Changelings. Yes, Satsuki is one of the unholy combinations, a vampirized Fey who kept her glamour-sensing ability. Thus cannot really be seen by those without the Sight. However, all of the business with Black Len, the Tatari, and White Len has more or less infused everyone with the Dreaming whether they can see it or not; so said Changelings dream glamour actually works on normal people non-fey without penalty; hence their Power Creep Power Seep.
 * The Tatari, btw, is a vampire turned dream chimera on steroids, and thus anyone can see or be affected by it once it reaches the height of power.

The Tatari "power-ups" of Miyako and the Maids are the result of Zepia Eltnam Oberon's original purpose
He originally wanted to become a Phenomenon in order to create the power to defy Fate; by randomizing the dice through chaos enough; a scenario could present itself that could defy the inevitable destruction he foresaw. Even if that chaos created monster upon monsters; eventually because chaos cannot be predicted it would result in a beneficial purpose as well.
 * This is likewise why Aoko restored this factor through creating White Len with his ashes; she's trying to create the ability to defy Fate as well.
 * In fact, the Chaos effect of the Tatari is why Melty Blood's "Satsuki Arc" is possible at all. Everyone's destinies from Tsukihime have been altered. Kagetsu Tohya stated that in dreams, all Alternate Universe occur simultaneously. Melty Blood was born from that nexus.

Tatari tried to use Kohaku's Nightmares, but her mind was Too Spicy for Yog Sothoth; and she received a bit of its power instead.
So the Tatari is a Dream Curse that uses people's Nightmares. Let's say there's a period of time where it enters the dreams of someone to copy their fears and Enemy Within. Well, it tried that with Kohaku; surely someone that traumatized would have some truly horrendous inner demons.

It tried to manipulate Kohaku's mind. What it encountered was The Doll; Kohaku's Will that completely shut off her emotions to Nothing. And as we know in the Nasuverse, Nothing is a very strong power. There was an dream war in Kohaku's head one night; and the result took control of that fragment of Tatari; and gave her some limited power to Shape dreams; hence the magic broomsticks and robots. Kohaku also subconsciously did the same thing to protect Hisui; Twin Telepathy being prevalent in dreams. However, The Doll was "damaged" sufficiently to change Kohaku's personality.
 * This was at the same time as; for some bizarre reason Tatari tried to do something similar to Miyako; but Miyako is too innocent to have any strong nightmares; and it's weakened state after the Kohaku attempt gave Miyako kung-fu powers instead. Just like Shiki; she imagined Kohaku's intelligence as "Mad Scientist / Wicked Witch". After this Tatari just went after more traditional targets.
 * Of course, this means that the Tatari lives on in Kohaku Even after they defeat Oberon, White Len or Dust; Kohaku is struggling with her piece. Yes, struggling. Remember, her trauma was becoming "The Doll" who took up the appearance of Hisui as a child; turned deadly. ...Mecha-Hisui. See the symbolism? And in Mecha-Hisui's ending; it always takes control.
 * I Knew It. The Melty Blood Act Two manga has Ciel commenting on how Kohaku is a Yorishiro for Tatari. A Shinto term for an object or being that can attract and host a spirit.

Kohaku knows the Tatari is trying to control her.
In the Melty Blood Manga, Miyako finds her diary, and it clearly states her strategy. (Even though Miyako doesn't understand the big words.) "Do not directly oppose the enemy. Find the enemy of the enemy and manipulate them into destroying them for you." It doesn't look like she's actually doing that too much in the manga, does it? She seems to be directly attacking the Tohno family. But what she's really doing in manipulating the destruction of the Tatari avatars she's creating. The army of Mecha-Hisui's that Ayako foresees destroying the world? Kohaku manipulates another Tatari event; Giant Akiha, to destroy them all; and then she has Arcueid stop Giant Akiha.

Kohaku has Agonist Syndrome.
Literal Power Born of Madness with a smidge of Demonic Possession? Ding ding ding ding! The demon that tried to possess her happened to be a piece of the Tatari, and she pushed it into Mecha-Hisui. This odd synergy gives her the ability to function.

Riesbyfe is a Lancer Servant.
So the Dust of Osiris, and a whole lot of Magi Babble; reanimated the spirit memory of Reisbyfe; but she needs a constant flow of Mana. And she's immune to Time Paradox. Gee, this sounds awfully familiar. Okay, what really happened was that Dust looked around at Alternate Universe and noted the Grail ritual; and through alchemy cobbled together her own version of a Servant and just threw the rest of the ritual away.

Melty Blood is a Fighting Game because of Miyako's Wish.
Okay, so Miyako was "too pure" for the Tatari to corrupt her dreams. And this...somehow gave her Kung Fu skills. However; in addition, this gave everyone Kung Fu skills, and it restricted battles to straight one-on-one battles where nobody took full advantage of subterfuge and trickery in direct fights nor did anyone make a wider range of battlefield. This is because this is how a Japanese child views fighting; ala King of Fighters. (Arcueid pulled off her "Moon" stunt when she wasn't in a "Fight Zone.")

Crimson Moon aka Archtype Earth summoned Ryougi Shiki to Melty Blood.
She doesn't want to be Crimson Moon, she wants to be Arcueid. She was happy as Arcueid. So she's hoping that Shiki Ryougi will be able to return to the origin her affinity to the Earth or else end her Crimson Moon self so she can be Arcueid again.
 * That would also nicely explain why she never manifests . Gaia has no power over THAT.

If Shiki Ryougi kills Archetype:Earth, this will herald the death of Gaia, and the beginning of Angel Notes.
Since Gaia hasn't been able to create a Type itself, it gave the role to Crimson Moon/Arcueid. Given the multiple Alternate Reality nature of the endings, this is probably not the Canon ending.

Shiki Tohno will be able to convince Archetype:Earth to return to being Arceuid
He did say he would in Kagetsu Tohya when he was talking to her within the dream.

OUR rumour spreading of the "Satsuki Arc" is what caused it to suddenly manifest
And I don't mean in the normal way, either. You see, after Tsukihime came out, people kept wondering why Satsuki kept getting the shaft and, somehow, the postulation that she must have an incredibly awesome arc of her own, the "Satsuki Arc", became a rumour. However, at the time, it was clear that such a thing was not going to be. Yet, the rumours persisted, taking on a life of their own. When Melty Blood came around and TATARI came into being, something changed. As stated above and in Kagetsu Tohya, in dreams all alternative timelines happen all at once. So, obviously, the collective 'dream' of a "Satsuki Arc" made contact with TARTARI during some point between Melty Blood's release and now. During that contact, TATARI made the malignant rumour, "Satsuki Arc" into a TATARI avatar, allowing it to come into existience here.

Of course, if this was true, it means that the "Satsuki Arc" is going to be bad. Really really BAD
 * And this would mean many, many fans of the game have had contact with TATARI and as a result, a secret batch of The Corruption, possibly his backup plan. Things are about to get really...really... bad.

Sion is a Covert Pervert
She's hardly ever seen, let alone talked to, a boy in her whole life. But she chose THAT as her outfit? She even gets mad if it's in any way questioned! One wonders whether this behavior is that much out of character.