How did someone hack my router from a game of Starcraft?

So, I was playing the game, Starcraft, with someone yesterday on the game's server (Battle.net) who claimed he could shut off my Internet for as long as he wanted. I thought he was bluffing, so told him to go ahead and do it. I wasn't even in a game with him by this point; we were just sending private messages through the game's server.

I thought he was BSing, until my Internet died... I checked my tablet, and the Internet was dead there too (so it wasn't just my computer; it was actually the router). I reset the router, but nothing. After a few hours of trying everything I could think of, the Internet came back on, but I could ONLY go on Skype (no web browsing, etc.). I have no idea why, because my tablet was working fine. It took my many more hours to get this working (I ended up using Google DNS, but I don't know if this worked or if it was just a coincidence).

Anyway, I wanted to know how the HECK this is possible? I didn't give any info to this guy... He said he "knew" my IP and he mentioned something about a RAT, which I found out might make sense... But I have a firewall (just the Windows one) and an antivirus, etc. etc.

So my question is this: how can this happen?? Could ANYONE I play a game with online do this?? I almost missed an online work training meeting because of this stupid event! I am a little terrified, as I don't know anything about Internet security... I didn't think someone could take my IP and shut down my router... Can someone explain how someone could do this?