I have my PC hooked up to the TV via HDMI, and I had no issues gaming on it with my dualshock 4 controller either :3. I've not dabbled too much into casting/streaming video from desktop to TV

(Plus I found the software for controllers on PC to offer way more capabilities/power than what I could do on the playstation, which is nice as I play all my games on controller even when sitting at my desk)