There are a few ways you can easily do this. For example -
1 - If your friend has a NVIDIA Card he can Stream through Gfeorce Experience Application, although I never used so I really can't tell if it's fast or not...
2 - If you two play mostly of your games on steam, there's an option on steam called "Streaming" or something on your account settings, enabling that it will allow your friend to stream his games to everyone on his friends list as long as someone accept the invite to watch it..
http://store.steampowered.com/streaming/
3 - You could both try other workarounds like Twitch or any Live Streaming software out there if you search for it...
Also SKYPE and TEAMVIEWER are not really made for gaming sharing they are mostly used...