I use it on my main PC (FX 6600, GTX 980, 16 GB of ram) and I play games. The only time you would notice it running is if you are gaming while someone else is streaming at the same time.
I use plex and love it. Especially before I allowed the kids to browse Amazon and Netflix alone. It is an awesome program and if your streaming device is not hardwired I highly reccomend makeing sure the server setting is set to your internet upload speed to avoid stutters or other buffering issues.