Installing new wires in room with hardwood floors

I quickly searched and found this on Amazon:

https://www.amazon.com/RiteAV-HDMI-Ethernet-Cable-Floor/dp/B075DC34V8?th=1

I’m sure there are others available. 

Here’s the thing, you want a box made for mounting in a floor, with protection, as to install a standard box, receptacle, and plate, made for a wall, would allow dirt, dust, and possibly fluids to easily enter. A box, receptacle, and cover made specific for floor mounting provides some protection. The rest, as stated, is pretty simple for your case (simply feeding from the basement).

I run my cables under the floor (via basement), and then route them into the walls near my equipment a foot or so above the floor.
It requires a little fishtaping, but the floors don't need to be drilled into.
B

And would be much cheaper than dedicated floor boxes and protective cover plates.

there are good reasons to utilize floor boxes, but they come at an expense to do it correctly.

Just poke them through. Avoid signal degrading  receptacles. Going cross joist, drill through.

Why not wiremold along the wall with a surface mounted box. There are many types to choose from...

https://www.crutchfield.com/S-XAvKqmCQqbD/p_717CMK50/Wiremold-CordMate-II-Cord-Organizer-CMK50.html?...

Go through the wall down to the basement by drilling through the bottom plate into the void between the floor joists. A flex drill bit will enable you to drill through the electrical box cutout in the drywall.