This is NO 1080p HDMI input on a 2005 XBR1 SXRD. The XBR1 is still a great TV, but a 1080p signal would need to be interlaced by an external source, passed though HDMI, and then de-interlaced by the XBR1 SXRD for the best results. For still scenes, this would look fine. For motion scenes, this extra processing would likely introduce a few artifacts (though most people probably wouldn't notice them).
This same analysis applies to both game and non-game signals.