It's basically what was said before.
The game looks far better in HDMI than it does in composite cables, CRTs have smaller screens with lower resolution and take up more space, and this is a 16:9 game you're cramming to a 4:3 screen.
I played the 360 version Call of Duty: Ghosts and Advanced Warfare in a 29' Toshiba CRT TV with 480p resolution. The numbers and small letters are confirmed unreadable, there's 1/10 of the screen missing on both sides of the screen, and there are black vertical bars under the game at all times. It wasn't nice. Especially since it was Ghosts, brrrr, what a terrible game that was
Not only do most if not all CRTs have no HDMI input while the 3 current gen consoles need them and they're your only option in 2 of them, even if you try to get a newer game running on them, you'll deal with crap like that.
All in all, leave your CRT for your older games and video games, like Melee, the SNES, rail shooters that use classic Light-guns...