That's what it sounds like to me.
I received a letter from unemployment today stating that I'm entitled to benefited from 5/08/16 does that mean I was approved?
yes get your money
More then likely yes. I would suggest to call and double check but honestly by the time they answer the phone you will probably receive the first card or check in the mail.
If the letter states that you are entitled to it, then yes, you were approved.