Definitely not normal. Our tiled shower floors do not have any give whatsoever to be able to press down on, the way I think I’m seeing in your video.

" Contractor says this is normal grout wear - is that true or do I push them to fix? "

You can push him to fix it as there are major issues caused by a poor install. I honestly do not know if you want him to rebuild the shower floor or not as he built it incorrectly the first time (obviously) and is already showing you by giving you a stroke job that he will no fix it by telling you it is normal wear and tear. 3 years it is probably out of warranty, but that will end up needing to be all ripped out I am pretty sure.

I have used them and I HATE them. Pick a 2x2 tile and sin no more.....

Wear a gas mask when you tear that out please. Grossest thing you've ever smelled, I promise.