If you weren’t told it was an alpha game you’d have no way of knowing. It sold a million copies while in alpha/beta, more than most other games ever made. The distinction between “alpha/beta test of game” and “game” is a distinction without a difference, especially for all the people buying it.
It was absolutely a game at that point, ask anyone who played it. Being blatantly unfinished doesn’t matter, it would have remained a game even if he never ended any of those features.
By this logic getting hit is a failure state, taking fall damage is a failure state, another player scoring points is a failure state, not actively getting points is a failure state.
If you restrict failure states to only mean things that end the game, then games like Dark Souls do not have any failure states, since in Dark Souls you always respawn when you die. Most other modern single player games would also not have any failure states, since they also let you respawn as often as you like.