Yes. You can participate anonymously or pseudonymously. I think we say in three places that we only give out contact details if candidates ask us to.
What, are you going to keep a record of the time I fiddled with it for an afternoon and then use that to disqualify me from a job?
Our incentive is to find reasons why you're hireable, not reasons why you're not.
What if I don't want to feel like my performance is owned by you?
Your performance is owned by you -- we won't have copyright to your code or anything. Signal we gather, though? Owned by us. That's the trade: we give you a really fun game to enjoy, but we control the universe you play in and, inside that universe, we control everything and see everything. If you do not like this trade, that's your prerogative and I respect your opinion. Nobody will force you to play Starfighter.