I am American, and I sometimes play computer games, but I've never seen/heard the word "tat" used in this way until now.

I looked up the original article in USA Today. Here it is:

The example sentence with "tats" is in a photo caption. The photo shows a young woman playing a video game. So I think Serg's answer is probably correct.

I've heard the word "tats" used frequently to refer to tattoos, never as a verb ("tats"). But in the photo caption, "tats" is definitely about playing video games, not tattoos.

I looked at the writer's bio, too, so I can see the writer is still a university student. So "tats out" is the gamer slang of a younger generation. (Younger than me, at least!) I tend to dislike slang used in the news but maybe the USA Today tech editor is from a younger generation too.

Google searches threw up two possibilities the footballers craze of tattooing themselves and the video gamers that Serg mentions, so I would go with that.

I have no clue what that means. I dont even know what american sport that pertains to

This is a guess because I'm not American <em>I do not know a lot about American sports</em> but I think it means to display "tattoos" on the players bodies, it seems to be popular amongst football players world wide today and is a craze in other countries and other sports. But please wait for the American answers.