Interesting choice of name, Tennis Elbow [official site]. How many other sports games are named for associated injuries? If creators Mana Games fancy branching out I've a few suggestions for them: Cauliflower Ear Boxing, NHL Broken Collarbone and Probably-Faking-It Football.
Mana Games, a French studio at least partly made up of amateur tennis players, have been making Tennis Elbow games since the mid-90s. Tennis Elbow 2013 is the most recent edition; as the name suggests it's not a recent game, but it did just crop up on Steam, so here we are bringing it to your attention.
My knowledge of tennis is not great. I know I'm not very good at it, although I once almost won a match against a semi-pro because he kept running into the corner of the court where I was repeatedly and ineptly serving balls, and slipped on one. Good work Shaun. Still, I've played a few tennis games at the more arcadey end of the spectrum like Virtua Tennis. Tennis Elbow is not as slick or accessible, but I still managed to work out how to play the demo with some degree of competence. I like that positioning really seems to matter: incoming shots are marked with safe and danger zones for returns, and when you do return the ball you can aim it using the analogue stick. This is harder to do when you also have to run to make a return, which feels authentic.
There is no trailer for the 2013 edition, at least so far as my bloodhound skills have been able to establish, so I'll do one better: below you'll find footage of an online match that should give you some idea of how the game plays. If you want to get an even better idea of how it plays, there's a demo available. Try before you buy is recommended, since Tennis Elbow 2013 costs $24.99 / €22.99 / £18.99, which is pricey for an older game.