The Chiefs tight end was out in Arlington, TX Friday -- where he swung by Globe Life Field to catch Game 1 of the World Series between the Rangers and the D-backs ... and where he ended up getting caught on camera indulging in his girlfriends catchy tunes.

First, fans noticed TK crooning and dancing along to 'Shake It Off' ... which was played during the game. Travis' bouncing around was actually shown on the jumbotron, and he didn't shy away from lip-syncing -- bobbing his head and getting a little hand action in too.

Later in the evening ... there was another opportunity to belt out some TayTay, and he did.

Check it out for yourself -- the dude was singing his heart out to one of her most well-known songs, 'Love Story,' and he was even seemingly recording himself while doing it. That, or he was on the phone with someone ... possibly even Taylor. 👀

In any case ... the timing of this great for a couple reasons. For one, it shows that he's all in on Taylor and supports her even when she ain't looking. Of course, the bigger deal here is the fact that Taylor just re-released her '1989' album ... and needs all the pub she can get.

Looks like Travis is solid boyfriend material in both capacities -- and funny enough, he's got a similar cheering style as she does when up in the stands.