No, you don't need an HDPVR.
If you don't have one already, please refrain from buying this, as you can get one with amazing quality and much cheaper than this.
This youtube video explains everything you need in under 2 minutes:
The AVerMedia Game Capture HD will work for you. This is a new device that has 1080i video game capture without gameplay lag while recording. This is standalone which does not connect to a computer at all.
I believe it is about $130, while the HDPVR is about 230+ (?)
Best of luck.