Why do Apple laptops have very strong performance regardless of whether it is plugged in or not?

Gaming laptops throttle a heck ton when on battery while MacBooks don't. Why is that?

Apple invests significant research and development resources for the purpose of creating state-of-the-art performance scaling and battery efficiency in its products. It's one of their top priorities across their entire product line if you look closely. There are entire teams of engineers, along with their commensurate engineering managers, project managers, and QA departments, who get paid to do nothing but think of and implement better ways of squeezing the most performance out of the least amount of battery power (and lowest heat dissipation), all day, every day. These are some of the brightest people in the world all coming together for one shared purpose.

Apple also has a key advantage in being able to cross-pollinate solutions between product lines, as these share much of their low-level software and, more recently, a significant amount of hardware. For example, an innovation in the xnu kernel that allows sufficiently low power consumption to allow the Apple Watch to have an always-on display can be reused to let the MacBook Pro turn off a significant amount of its electronics when there are no user-visible changes being drawn on-screen, allowing a significant energy savings without compromising performance.

To your specific point of good game performance on battery, there are many, many contributing factors. One in particular is dynamic frequency scaling and clock gating: Apple spends significant engineering effort on tuning algorithms that will raise & lower CPU and GPU voltage, and enable & disable CPU and GPU cores, to precisely meet instantaneous demand for these resources. So when you need responsiveness, you can quickly get it, and when you don't, much of the silicon quickly turns off and saves power, allowing you to run on battery for half the day instead of burning through it in an hour.