Not watching that since I'm not that far in the main game yet. I've just been running all over London looking for ways to get Evie messed up while occasionally doing missions :3
So far, the fight club stuff is nice but it's too bad that it fades out before the full animation can play. I suspect that the animations end with a kill which is why it stops short. Maybe later on the fight clubs become fights to the death so you can see the full beatdown? Hoping that's the case. Anyway I've found 4 different ways Evie can get finished off, three different fighters each have their own and one has a reversal finish. Hope there's more.
As for the regular stuff around town, normal thugs do have their own kill animations. I know everyone has a basic finish if you just let them wail on her, and some have reversal finishes if you attack them while they're guarding. However I've seen more that I'm not quite sure what causes them, maybe it has something to do with which direction Evie is facing when the finisher starts. Enforcers have a particularly brutal one where they force her to her knees and stab her through the neck.
As for the thugs, this year we have female zako so of course there's a lot to see there. Stealth kills, normal kills, reversal kills, double/triple/quadruple kills, and many differ by weapon (3 different weapons) and wall proximity. Or if you prefer the non-lethal variety there's still knockout holds and OTS carries. Also you can restrain them, shove them into carriages and take them across town for fun.
All in all Evie's a fox and I'm loving the game.