Persona 4 Arena On Hit Effects

[Kosheh]

they're particle systems at work. it's the magic of modern-day console rendering circa 2003 which they use to animate highly chaotic systems of fuzzy phenomena through the directions set by an "emitter"

in english, that basically means "how they make fire look cool in videogames"

they're rendered in 3D, so basically, yeah in terms of ripping things from fighting games it's more or less programming.
I'd assume you'd have to use a 3D modeling program in order to extract them and even still, it'd be an animation so much as an actual tangible texture or sprite that you'd rip :/