Feel the fear and play variants anyway

...then I would say...

960

is Sumo. No weight classes, and if the other guy is a lot bigger than you then you're probably going to lose no matter what you do.

Antichess

is Karate. Shotokan. All very rigid, and one false move leads to a staccato sequence of you getting punched, kicked and beaten.

Three-check

is Wing Chun. You're always looking for an opening from a confined space. Fighting in a phone box, if you're old enough to remember those.

King of the Hill

is Aikido. Focus on your one point at all times and you will be amazed at your own power...assuming that the opponent has some idea what he is doing, and if not it's easier just to hit him.

Horde

is Tae Kwon Do, you *could* use your hands but in practice you don't...it's all about who does one particular thing well, and can find a way to do it that the opponent cannot conceive of as possible (wherein promoting = kicking).

Racing Kings

is Tai Chi. You don't need to be big or strong or athletic to defeat your opponent...it's all about seeing the fearful symmetry (OK I don't think Wm Blake knew Tai Chi but, you know, poetic licence).

Atomic

is Muay Thai. You WILL get knocked out in a split second unless you have a pretty good idea of what you are doing.

Crazyhouse

is Jiu Jitsu. As future Hall-of-Famer Jordan Mailata said of the NFL playbook, it's like a one-hundred sided Rubik's Cube. GMs who dip their toe in the zh waters run the risk of getting hip-thrown and arm-triangled by someone who, in the ring, they'd easily turn into a pancake.