Thank all of you for your suggestions! I was able to play with all of them in person.
I ultimately chose an Olympus TG-4, despite me being a Canon loyalist.
Here's why:
Pros:
Waterproof/shockproof/dustproof. My dad will be carrying it in his pocket, so lint WILL get into the mechanism of most cameras.
NON-retractable lens, no flimsy lens covering. Again, he's going to abuse it. The retractable lens will be extended while he carries it, even if it's wedged inside a pants pocket or airplane seat pocket (where he lost his last one) and the retractable lens covers invariably get stuck with his handling of it
Internal charger. No need to carry an extra charger around, just a proprietary (UGH!) USB cable. At least the cables are cheap enough off Amazon to pack a few extras. Even at that, generic extra batteries & external chargers are also cheap for this camera.
Covers have 2 locks + rubber seals. The Fuji waterproof camera I looked at used friction-fit only. The more um... idiot proofing.. I can get with this camera, the better it will be.
NO touch screen. To me this is a big pro. I've used cameras where all physical buttons have been removed and it stinks.
1080p video. Does an admirable job here.
Cons:
Proprietary USB cable. Seriously Olympus? It's 2016. With the exception of iCrap, everything else has standard USB cables.
Image quality. Probably not bad, maybe even very good for this type of camera, but I'm used to my DSLR. It's not my DSLR by any stretch of the imagination. It'll be more than enough for dear old Dad though.