It's a nice theoretical implementation but few practical examples would be found using floating-point math, running as they are on systems that don't support it.
Unless your chip has a hardware floating point unit, you're stuck using software float operations. They're slower, though not extraordinarily so. But the main drawback is the floating point library can massively inflate your code size to the point that it no longer fits in available memory.
If you can get away with it, it's fine, but when you can't it's a huge problem.
There's still a few reasons not to use it, though. Saving and restoring the float registers adds interrupt handling overhead. If you can fit into 16 bit integers, you can also use the 2 way SIMD instructions and get at least double the throughput.
Finally, floats themselves have a lot of footguns. You have to be very careful about propagating NaNs etc into control loops. It's also really easy (in C) to accidentally promote to double.
You don't need the fine precision or large range that floats have (we get those using exponents). Signal variations below a certain threshold are drowned out by the noise floor. Signals in control systems also have an expected maximum bound.
At other end, stability calculations based on quantization noise may be difficult with floats, since their least count changes with exponent. Fixed points have a uniform LC throughout its range.
Both are useful.
My reaction was a similar "Huh - makes sense".
I would be sure there's plenty of applications for PIDs in a game engine itself - a quick search turns up things like self-balancing physics objects, making game entities turn to follow a mouse pointer, and so on.
It could be a moving enemy, flying robot or a spaceship, rotating gun turret, maybe even doors which need to be moved to desired position.
Even without physics engines PID controllers can be useful in games for making procedural animations. Having an object suddenly starting and stopping a movement doesn't look natural. It looks much nicer if initially an object slightly lags behind, slows down closer to target and maybe even slightly overshoots the target. It looks more natural because that's how things move in real life even non mechanical things. Try quickly swing a hand and then stopping it, you will see a little bit of overshoot/oscillation at the end.
PID controller isn't the only solution to the situations described above and sometimes it's an overkill. Sometimes you might just script or animate certain behavior. Sometimes you might use a simplified control model. Sometimes you might implement P, and intentionally or not achieve other components by adjusting physics object properties like friction (unfortunately you can't easily change physics properties in real world). With regards to animation example similar look can be achieved by directly animating it and any good animator will be familiar with things like ease in, ease out and overshoot, that's fine for static animations but games are interactive so it's nice if things react to player movements. Procedural animations can also be achieved by simply using the physics engine and letting things dangle, but that will probably be more computationally expensive than simple PID controller, also harder to constrain and prevent violent shaking in case of unexpected collisions with other world objects especially when some of them are manually animated.
Each approach has their own tradeoffs. And which one gets chosen will depend on the specific situation and skillset of people making the game.
There are couple of factors that make using a PID controller in games a bit easier compared to real life. In games you can usually directly read the exact positions and speeds of all objects, you can generate force out of thin air, you can generate unrealistic forces and if something goes wrong you can simply clamp the numbers. In games you also choose at which level to operate the PID loop thus making tradeof of code complexity and while still getting benefits of nicer looking animations. In real world you might want to control position of flying quadcopter while the thing you can directly control is speed of propellers with linear velocity, linear acceleration, angle, angular acceleration being between without a way to skip them.
Often these issues can be handled with very careful floating point order of operations (so long as -ffast-math isn't used...) but since its all implicit it's very easy to get wrong, while in fixed point you're forced to confront the scalings of different variables explicitly.
There are also many cases where floating point is the clear winner, but again, you should think about it and not just choose floating point reflexively because it seems easier. Its convenience makes it very easy to sweep errors under a rug, and they always come back to haunt you later.