Hi BoingBoss,
If you have a graphics card and an 040 then you might be lucky, mainly thanks to the graphics card.
For I know that in my A1200T I had in 2002, it struggled to play the .AVI files supplied on the OS 3.9 CD.
I was using AGA and had a 50MHz 030 on board.
Why did it struggle? It played them in black and white and they were of poor quality, quite jittery.
This was the case, even when my Workbench screen mode was set to 256 colours.
Thankfully, you have a graphics card and a more powerful processor, which just might save your ass and let you play MPEG files of a reasonable quality.
Players - No idea here. Does Frogger play MPEGs?
I'm quite out of touch with more modern Amiga software like this, as I never really had a powerful enough Amiga to run it on before I called new Amigas a day back in 2002.
Good luck anyway, I'm sure you will find something in terms of software for you to successfully play these files, and I'm 90% sure that your hardware is powerful enough to do so, albeit not perfect quality.