well as that video says,you should define a bunch of rules that define the genre and then see how well the game fits those rule
fighting game basic rules would be
- two character hits each other with stuff
- this makes their health decrease
- the first one that get it's health to 0 lose
- a timer decide who wins in case nobody gets to 0 after a while
smash bros already fucks one of the basic rules of the genre by having no health bar and having this weird weight based system
then i guess you could add some advanced rules
- character can block other attack reducing damage
- character movement is limited
- fighting is limited to a flat zone
- most fighting games have a combo system
now the biggest one here is about movement,smash bros doesn't control like a fighter at all,it controls like a kirby game which is why they could do a story mode that features barely any fighting at all,sure character can block but it's not like blocking is ingrained as in other games,when you see a smash bros match it's about the character dashing and running all over the place,certainly not standing their ground... there is a reason it's "fox only" and it's because fox is the guy who runs all over the place like an idiot,that video argue that you can combo,i say that it's pretty bullshit because after a while character starts to fly all over the place and you can't do combo when that happens,one of the basic of a combo system is that the stage usualy has boundaries in which you can trap the opponent but in smash bros there is nothing like that,that is another thing that makes it unfighter like
the reason that most fighting game takes place on flat zone is because the character themself have stiff movement,so the problem isn't that stages like rainbow zone exist and that if we ban them all the game suddenly turns into a fighting game,the problem is that i can triple jump high enough to reach the top of the screen
the rules of a party game are less defined but one perceived constant is randomness,randomness is bad because it means you can lose even if you are awesome at the game (see the penny arcade strip above) that is a pretty stupid argument but let's not go off road... so how's smash randomness?
- a player who can gets hold of certain items has an advantage,if an item spawns near to a player instead of the other that player got an advantage
- lot of things explode in smash,in fact it's possible for a player to die even when his opponent has done nothing other than standing still
- tripping
- super special moves aren't dictated by thing like damage received and dealed but instead by a balls that appear at a random time in a random spot,one interessing thing to note is that party game love losers,did you know a free super special is granted to a player who's behind at least 5 points? isn't that sooooooooooooo unfair? i think i read once that mario kart has a similiar system too were player in the last place are granted better items
while the game is not totaly random like mario party,there is enough randomness to bother tourneytards and it's a pretty heavy component,disabling it doesn't turn brawl suddenly into a fighting game in the same way playing mario kart battle mode doesn't turn mario kart into an arena shooter,oscar says wipeout should count as a party game but i tought most of the randomness came from missile and shields? for example is there a wipeout item with the same power as the hated blue shell? (this is a serious question,can't say i like racing game) if the element of randomness in wipeout is not really estabilished so much then it's not a party game,just having a small randomness element (items falling at random) doesn't suddenly turn into a party game but when that random elements become more prominent (lot of items start falling at random,one of the items make you invincible,one of the items instantly defeat the other player even if you were losing) then yes it start becoming more a party game

ah see? the third strip? that one is a party game
but as i said before the problem is not "that banana is not a fruit" the problem is "fruit are better than vegetable,therefore even if there are some elements that might let you think this is a vegetable and not a fruit,i'm going to argue it's a fruit"