Depends on what games and whether the app in question is a Universal app
I play music games all these years (12 years now and counting!), started playing the mobile music games on some Android phones (e.g. Xperia Z1) and then sticking with my Air 1 for about 3 years before going over to the 12.9 inch iPad Pro.
I must say that the screen size alone plays a big part in changing the experience greatly. It will take time getting used to looking at the big screen; expect to miss out sometimes if you are too focused on the part of the screen that used to be the full screen of the 9.7 inch (i.e. the edges). Also, get used to operating the big screen: what games you play will affect this greatly. Most games I see should benefit from this (e.g. being able to make more precise moves in puzzle games) but for the games I play, things are more interesting.
You see, the games I play involve tapping and swiping/sliding at moving objects at precise timings. The big screen means screen elements are more spread out, allowing me to stretch out my hands more and thus play more comfortably. The play areas are now considerably bigger, allowing me to interact with the objects more easier, which can mean the difference between a full combo (i.e. tapped all notes correctly) or another combo break. But conversely, when it comes to swiping, I need to swipe faster as I need to cover bigger physical distance over same period of time as before. It's a give-and-take in other words.
Also, consider the hardware used inside the iPad Pro as compared to what you have. The jump from A7 to A9X and from 1GB DDR3 RAM to 4GB DDR4 RAM helps a lot too in making gameplay smoother; I had random stutters in certain games on the Air 1 that cost me losses in the games
. There is virtually no such issues in the iPad Pro, even when recording the gameplay (which does use up computing power on your iPad too as it needs to also push video output to the Lightning AV adapter along with operating the game)
Finally, you will need to see if the app is "Universal" or not, which means whether the app is also built for iPad too. Simplest way to see it is to see if the app appears in your Purchased tab in iTunes/App Store without changing to show iPhone only apps. If the app is Universal like most apps, the content will be already sized nicely over the entire screen. Things will look as sharp as on smaller screens. If not, you will see a circle with either "1X" or "2X", press that and the content will be stretched out over the screen as though on a 9.7 inch iPad (i.e. not fully over the entire 12.9 inch screen) with black bars around the rest of the screen, which looks bad.
Hope this helps in your decision!