The process showed it was owned by WindowServer, and launchd (1) owned that. I didn't want to try killing WindowServer at the time, instead I just chose to restart. I'm not 100% certain that the EyeTV app did turn into a zombie, but OS X wasn't letting me relaunch it as it thought it was running, both via the Dock icon with the triangle below it and ps.

Overall lesson learned from this was that it was much simpler dealing with the ReplayTV hardware then it is a PC based solution for recording live TV.