I got it installed (grabbed it from the Plex site), and whilst it runs, it runs like a dog on my MCM. Given the lack of processor power and memory in the device, that’s not so unexpected though.
Looks like you’re seeing something similar, your first movie is either too high resolution and/or needs some kind of transcoding for your Bravia to play, and that’s beyond what the MCM can handle. The second movie is much simpler and lower resolution, so the MCM can basically just stream it without problems.
You should be able to confirm that perhaps using the DLNA option instead - see how your first movie does with that, or perhaps try recoding it into another format that you’re sure that the Bravia can cope with using something like Handbrake.
But fundamentally I think you’re hitting the limit of the hardware, hence why we’ve not had the Plex app until recently. But the MCM itself if used as just a fileserver or as a limited DLNA server works well enough. I use it with a Pi1 and Kodi to feed a dumb LG TV, and it does the job fine (although most of my rips are standard DVD and not BluRay, so I don’t push it too hard either).