Extreme blockyness of in particular red areas is quite common when encoding video material. Now I don't know much about those Hybrid-TVs but I could imagine that due to the nature of gaming being fast movement lacking motion-blur at high fps @ progressive (where TV stations are usually broadcasting interlaced) video material your TV might use a faster but less nice looking way to upscale and/or "display stuff".
Also note that TVs are of much worse quality (like... very poor pixel density) than actual monitors and I've heard that these hybrid TVs often are intended more to be a TV than a monitor. If you ever tried to hook up your PC with an actual TV you know how awful it looks.
In any way, try making sure you run the game at correct settings (like fps, vertical sync on/off, resolution etc)... the TV manual might/should contain some information on this I'd guess?! Try running the game in the TVs native resolution - and/or try not doing that --> I could very well imagine that the TV for e.g. is basically a 1080p model, but might be unable operate at that resolution in gaming mode - instead there it would only operate at for e.g. 720p (again, consult the manual).
Sorry for all the vague information/suggestions.
