If you measure it and it is less than 10m (the physical limit of hdmi without a repeater) then you might consider a floor cable canal. They usually come in a variety of colors, don't require adheisive or screwing and are just simple things to keep people from tripping on cables

I have one of these on a doorway, to connect a pc to a tv and it works good enough
If you don't mind getting games outside of steam and tinkering, Need For Speed Underground 2 is my favorite racing game. There are different types of races, deep car tuning/customization and a decent world to openly drive around in. And a banging soundtrack too.
I haven't played it, but I have wishlisted Sonic racing CrossWorlds because apparently it is a great alternative to Mario Kart, with local co-op.