Isn't NDA on something that is "free" kind of irrelevant at this point?
Nope. Lots of games employ "free" betas leading up to their launch, and if an NDA is in effect, they will enforce them like nobody's business. When ESO went into beta weekends late last year, they were banning people left and right for violations of the NDA, up to and including streaming gameplay on Twitch.
Having an NDA is completely unrelated to the cost of a product. There are a lot of reasons why an NDA is implemented - testing specific features, not the full product, the unfinished nature of many betas, etc. Another reason for enforcing NDAs is to prevent competitors from taking your ideas for themselves and potentially beating you to market with them.