Thanks for flagging this, and sorry, that wording is on us. Playing doesn't need an account: the Play button opens the game straight away, and you can leave a thumbs up or down without signing up.
The sign-up box only appears when you go to leave a star rating, or after 5 minutes of play (with a "Keep playing" button to close it). Ratings are tied to an account with a confirmed email so people can't post fake reviews, but you never need one just to play.
Clearly the page didn't make that obvious, so I'm changing it to say an account is only needed to rate. If you hit the sign-up screen somewhere else, could you tell me where? I'd like to fix it.