I have a variety of PCs throughout the house using JRMC15. They all run it well for video and audio. The highest spec'd PC is an i5 750 (quad core, 2.67 GHz), 4 GB RAM and 2.5 TB disk space, with an nVidia 512MB 8800GT.
The most lowly is an Acer Revo 310 with a 1.6 GHz dual core Atom with an Ion graphics chipset. This small form factor PC runs theatre view just fine and can even decode Dolby Digital TrueHD and pass on the LPCM to my receiver.
I'm also running an Opteron 180 in a socket 939 mobo that has both PCIe and AGP, running with 2 GB RAM and an nVidia GT240.
My main HTPC is an i3 530 on a Gigabyte H57 mobo, using onboard graphics and 4 GB RAM. This only has 30 GB storage in an SSD, but all these PCs are connected to the 27 TB server by wired gigabit ethernet - and that contains ALL my media.
There's also a laptop or two somewhere and the have ATi/AMD 3000-series video cards. Therefore they can run all the video files and TheatreView just fine, also.
As you can see, a beefy CPU isn't necessary, but it will make elements of the GUI more responsive, for sure. However, even the Atom with Ion graphics can take care of some of the most demanding h264 video decoding. Audio-only files are a breeze, even 5.1 DTS files in a wav container.