i didnt buy/ or got beta key? I just saw an install button, installed and pressed play

if you set up on the battle.net site for beta access they will eventually/possibly give beta access to your acc

i thought i have to insert betakey somewhere? I remember, they will send email with a key to you? I didnt get or do anything

It happened to me as well. I just setup my beta access on my Battle.net acc for the games for Beta and it worked no key needed or anything

You got invited by blizzard they keep sending out random invites. One of my friends got randomly invited as well. grats man!