First thing's first: Panem Run doesn't have a lot to do with The Hunger Games at all. As an "endless runner" game, it has about as little connection to the franchise as you could imagine. You play as a non-movie character and run through various environments modeled after the different districts in the Hunger Games movies and books. But while the game is thin on lore, it remains an enjoyable entry into an increasingly crowded genre.
As in other similar titles (most notably Temple Run), your character sprints forward with reckless abandon, and it's up to you to provide timed input to bypass obstacles while collecting money and loot. Swiping upward prompts a jump, swiping downward leads to a slide, and swiping left or right controls your position on the track. The challenge comes with trying to combine these commands in close succession, and if you're tasked with jumping, moving sideways, and sliding within a second or two, there's a good chance you're going to mess something up.
When this inevitably happens, your run stops, and you are offered the option to pay a bit of your winnings for the ability to restart in the same area, or simply end the run and start fresh. The fee for getting back on your feet grows with each failure, so sooner or later you're going to need to throw in the towel and start a fresh run.
There's a relatively deep skill system that lets you level up certain abilities by collecting various supplies found on the track, but this can also be bypassed by simply paying for the upgrades using the in-game currency. None of the upgrades provide a drastic change to the overall gameplay, so if you choose to ignore this part of the game menu entirely you'll likely not notice too much.
It's a free-to-play game, which means there are also in-app purchases. Thankfully the store options at this point are simply coin packs, and since the game rewards you handsomely for even the most modest of runs, you probably won't find a huge need to crack open your real-world bank account.
As I mentioned above, The Hunger Games: Catching Fire: Panem Run (yes, that's its actual full title) doesn't do a whole lot to provide an extra thread to the Hunger Games story, but the mechanics of the game itself are solid enough that you'll likely get a good bit of playtime out of it. It's a fine time waster while you're waiting in line for tickets to the new Hunger Games flick, just don't expect it to catch fire.