This appears to be a reimagining of Prince of Persia 2 from 1993. I never played the original Prince of Persia 2, but I've seen statements like "Remake of the second game with different graphics and levels"; so maybe only the gameplay style and plot remains. It's a 2D platforming game, often in a simple maze, with some basic combat.
The Prince looks like the Prince from the Sands of Time series although he doesn't have any sand powers. You can revert to checkpoints using limited Revive potions (and it looked like there's a store to buy more - classic microtransactions - although I had more than enough to complete the game without trouble). There's also healing potions to restore health, and I had a good stockpile of these. You will find potions in the levels if you explore, but the Revive ones are much rarer.
From my experience, games on the Kindle have always been basic since the controls are pretty limited, but I was actually really impressed with this. You move with gestures with your left hand, and some actions are performed with the right. You swipe up and down to climb, running then swipe up to leap. Then you can hold the right-side then swipe left/right with your left hand for a safe jump. Swiping down with your right crouches, then movement with your left will roll, which is required for some traps.
An aspect that makes the gameplay much smoother than I expected was that the game is pretty lenient how close to a ledge you need to be. So if you are below a ledge and swipe up, the Prince will step/turn as required to actually do it.
When you are near enemies, you can press the on-screen sneak button, then move towards them. If you reach them undetected, you auto-kill them. Otherwise, you will engage in combat. The Prince automatically draws his sword, then you can swipe the right-side to perform various attacks. Movement is with the left as usual, although most combat situations will be fine for you to stand still. There is an on-screen button to defend, and timing this will counter-attack, stunning the enemy to allow you to combo them. There's a few set combos, and performing them successfully will be indicated to you with the name such as "Tiger Thrust" appearing on-screen. You can have 2-vs-1 fights, so you will need to swipe left/right to turn to face the desired enemy. The enemies tend to wait and take turns to attack, so it's not like it requires high dexterity.
There's many branching paths in the levels, and you are told the percentage completion at the end of the level. Some paths are more hidden such as when the ceiling is at the top of the screen but then there might be a small gap. There were a couple of levels where this was actually the correct path, so I'd imagine some levels could frustrate people if they don't spot it.
It's a short game, and the in-game time said it took me 1 hour 41 minutes. Each level is short for a quick play session so was also well-suited to the Kindle.