Sorta. There's actually 3 things that can fail on an AIO, although only 2 are normally thought of. 1) fan failure. Common, it's a fan, it happens. 2) pump failure. Motor or diaphragm gives up the ghost. If the motor quits, it's a dead giveaway that it's dead, if the diaphragm goes bunk, the motor still runs but nothing moves. 3) most common in aged AIO's and most overlooked is fluid levels. The fluid evaporates over time, usually around 4-5 years depending on how hot the fluid gets during extended use. This puts very little fluid in the radiator (which is also the reservoir) so cooling efficiency hits rock bottom.
With high idle temps and high load temps, I'd be thinking it'd be #3, there's simply not enough fluid in the radiator to effectively cool the cpu, and as soon as you put a load on it with a game, it's heading into thermal shutdowns. The fluid should normally at idle be the same-ish as idle temps, low-mid 30's, but that's not happening, fluid temps are prolly closer to 50-60°C which lowers efficiency even more.
In a nutshell, it's old, worn out and needs replacing.