I would recommend allowing people to just pick a name and hop in. One of the keys to the success of web games is that there's (often) literally no barrier to entry, including the need to create an account.
Also I suggest making it really easy to invite someone else to play with you by sending them a link. That's more complex though.
Also since you already have a spectator mode, it'd be cool if people see an active game when they go to the home page, like lichess.org. That might be even harder to do that invite links.
I second this. The likelihood that I'll try the game out is drastically increased if I can enter a throw-away name and quickly start playing.
You could automatically assign a throw-away generic name, and then slap a 'try it right now' type button prominently on the home page. If the game is good, then I'd be willing to create an account.
You could also do a "link to Steam" option or something like that in the user settings menu. So if someone is interested in continuing to play, or even just persist a user name, they have the option to link it to something more permanant.
I opened a tab to give it a try, but backed out when I had to provide an email to see how it played. Assuming I enjoyed it, I'd then be motivated to make an account to keep track of my play.
My experience is that almost 100% do sign up. Signing up is not a barrier. Funny statistic I had in a game was that while almost 100% did sign up, only 50% of those entered the game. After highlighting the "enter game" button, that 50% went up to something like 85%. But the takeaway is that almost everyone do signup almost automatically.
