He's been cast to play Hank Williams in a new biopic, and will be singing in it. So he's doing gigs to prepare, because British actors are method like that. He was at a musical festival, and someone got a video. They also got some parenting in there, so it's not the best audio, with the fighting children and annoyed adults. But you can hear Tom.
It sounds like his voice was strained (too much practising? Nerves?) but the guitar playing seems legit. I am not sad to have more Hiddleston singing in my life.