You are splitting hairs here. An alpha/beta of a game is a game too

Alpha/beta is an arbitrary line in the sand drawn by the developers. Notch could have woken up one day and decided that the state the game was in was final and call the game done.

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.