Thank you for coming over to our side of thinking and posting this.

2-factor authentication (2FA) protects against keylogger hacks by effectively changing your password every 60 seconds. So, if you're unknowingly running keylogger software on your PC, your icedrill.io account should still be uncompromised and inaccessible to those hackers. Everything else without 2FA is still at risk to keyloggers though (e.g. Bitcoin-QT).

Small correction here on your notification: Gmail is not a requirement. You can create a Google Account using any email address, and use that to sign in to any service which supports Google's OpenID implementation.

EDIT: I'm still a bit confused by your post. You change your mind (which is obviously in tune with current online security practices) to support the initiative by linking to an example which is clearly covered by our decision, but then state that our decision on this was arbitrary/capricious?