This game spawned all kinds of genre imtators (Mortal Kombat, Fatal Fury, Killer Instinct, Tekken etc.) Excluding boxing, wrestling and martial arts games, was Street Fighter II: The World Warrior the very first game of the tournament fighting genre? What was the original Street Fighter game like?
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"The sun is shining...but the ice is slippery."
There were similar games before it: "Yie Ar Kung Fu" and, as you already mentioned, the first "Street Fighter". Both had the life bars and the sideview perspective.
"Yie Ar Kung Fu" had a strange control scheme though. The NES version is much closer to the "typical" gameplay in "Street Fighter II".
"Street Fighter" in theory already had the typical stuff: Two out of three rounds, a time limit of 99 seconds, three punches and kicks, character-related stages and the special moves. However, the actual execution was totally crappy.
One thing that was introduced by "Street Fighter II", as far as I know, is the fact that you can choose between various totally different fighters. "Yie Ar King Fu" only had one fighter with all the opponents being computer-controlled. And "Street Fighter" had Ryu for player 1 and Ken for player 2, again, with all opponents being computer-controlled.
If you want to know what the games are like, you can either play them on an emulator or simply look for a gameplay video on YouTube. "Street Fighter" is for arcade. And "Yie Ar Kung Fu" exists in two different versions: For the arcade and for the NES/Famicom. (Both games are different and the NES game is not really a port of the arcade game. It even has another protagonist. So, in this case, you should watch both versions since they are basically different games and both precede any "Street Fighter" game.)