Yeah basically it is stream your screen online and taking their input and streaming that back to you. It can handle up to 4 players on a decent connection but you would need a very good wired connection for more. Only the host needs to own the game.
There is nothing dodgy, its all in built into steam, so if you are happy enough to leave them alone playing a game online chatting with their friends, its just the same really. They can only talk to their steam friends, noone outside can join without an invite.
The lag and stuff really depends on how good your wifi is and how good their friends connect is. A decent connection should be able to stream 1080p at 60fps with voice chat.
This is the sale page for when they launched Remote Play, all these games are meant to work on it
All the lego ones are there, including the Harry Potter ones.
It uses the same tech as Steam Link, so you could set up steam on the laptop, and hook up steam link on a phone and try it around the house to test the performance.