I used to do that but you can record screen video with the Snipping Tool now. Works fine, mp4 file as output.

Where I’ve worked Game Mode was disabled by GPO in enterprise environments.

Disabling a built-in, non-networked feature and then replacing it with a cloud-linked, self-updating 3rd-party one doesn't seem like it would improve security.

They were using on-prem Atlassian, no cloud link and no self-updating, of course.