You should be able to, just look into setting up a virtual private network. I'd suggest using Logmein Hamachi if you want to go with something simple. It lets you create a virtual network you can access with a password, giving you all the same features you'd have locally.

You'll certainly get better performance with a local LAN but these days most games are playable via the internet anyway. Which might really be a better option, if the games you want to play have usable online multi-player functions that could save you a lot of trouble.