Possible? Yes. Usable? Maybe, it would all depend on the internet connection of your home and where you're at.
A major difference between LANs and WANs is that WANs are shared resources, and LANs are dedicated to the owner of the network, normally. You can try it, but it's all going to boil down to two things: 1) How good the internet connections are between you and your desktop; 2) How many other users on the nodes you and your desktop are on are attempting to use the connections at the same time.
Video services, (such as Youtube, Netflix, Vimeo, and more), already have a compressed file that they're sending you when you stream the video from them. It's the same file over and over again, so they can send you as much as possible to buffer it when your internet starts to drop.
Games tend to be live, and highly detailed for the more modern and fancy ones. More details require more processing power and bandwidth to transfer. And since everything is on the fly, if your internet starts to lag, then you're going to be loosing frames.
A few years ago I tried to use LogMeIn to play Wow at work, and the frame rate was bad for me; however I was only on a 10Mbps connection while at work, so a higher speed internet would have helped.
I've tried screen sharing to a home pc from abroad. It runs at about 1 fps. Aka, not nearly well enough to play any game. You'd have better luck just playing it on your laptop. However, I was using teamviewer, but I doubt you'd have much luck with any other screen sharing solution. Just try pinging your home ip from abroad. You'll be lucky to get below 100 ms, and that's not counting download and upload speed. There's just not enough bandwidth to send that many frames. That said, please do share if you come up a solution – Blaine – 2016-06-27T02:58:12.323