I don't know what your apparent idea of version classification is, but here's mine.
Think of beta being: the game is doing but its supposed to do, but we still need to iron out the bugs. e.g. v 0.5
Alpha being: the game is finished. e.g. v 1.0
Alpha, Beta, Gamma, Delta, Epsilon, etc.
Beta is like second place... not quite
Alpha is like number one... where it should be
This is not called "Alpha", this is called "Gold", when the product is finished and ready to be shipped.
As explained above, Alpha means the very first working version, with missing functionnalities etc... and Beta means full functionnalities and full of bugs
