No, the original Pi B can play 1080p video just fine. The video is not decoded by the CPU. H264 and older codecs play just fine. It cannot handle h265 videos as it doesn't have a hardware decoder for those. Kodi works just fine in fact. The interface is a little bit slow, but actual video playback is fine.
You can look into inform6 and inform7 (totally different beasts, they are not older/newer versions of the same thing), TADS, or something like Quest perhaps. There should be more but these are the first that come to mind.