The damage is probably not too severe (aside from the $300 lost to your Steam account.)
Signing up for credit cards (especially online) in Canada requires more information than just your address, your name and your phone number (especially an old one that's no longer in service.) In particular, they would need at least your date of birth and your SIN, for example. So, they can't just sign up for cards and not pay them with this info.
However, the fact that they broke into this account means they know the username and password you used here. If you used the same password elsewhere, they may be able to break into those accounts as well, especially if the username is similar (ie: your email address.)
So, if you haven't already, you should change the password on your Steam account. You should also go through other online accounts and change those passwords as well, particularly if they use the same password as Steam. You may also want to consider two-factor authentication where available (ie: Steam has the Steam Guard app that can be hooked up to your account on your smartphone.)