Can my tv play games in 1080p?

If a TV supports it and the device you connect to the TV through HDMI can output a 1080p signal, yes.

Looking through all the details from the company's site on that model, it's rated for 720p. A number of different reviewers/purchasers on other sites say that it looks great at 1080p.

HI there,

According to the company's specs on that model - these are the HDMI resolutions is will support

[table][tr]HDMI Input Signal Support[td]1080/24p, 1080/60p, 1080i, 720p, 480p, 480i[/td][/tr][/table]

I have a Xbox One X and play on a 1080p TV. As i can not afford to get a 4K tv at the moment. They are expensive in my region.

To a degree you don't need a tv that supports HDMI 2.1 to play supported games 120 FPS.

I bought a 4k/HDR LG tv about three years ago and it's HMDI 2.0 but it doesn't support 120FPS at 4k but if I went into the settings of my Xbox Series S and X and changed the resolution from 4k to 1080p I can then set FPS to 120 as my consoles tell me I can play 120 FPS games at 1080p.

Your tv may not support 1080p. So switching to 1080p, will cause the image to be slightly distorted. The game was probally designed for 1080p so it has to have the bars to play in 720.