While that code was an excellent way to show what's going on, I usually wouldn't use code like that. If it had to be fast, there are usually even faster solutions, such as using SSE on x86 or NEON on ARM. If none of that is available, sure, I'll use it, provided it helps and it's necessary.
By the way, I explain how it works in this answer
Like Skylion, one thing I've used a lot is figuring out whether a number is a power of two. Think a while about how you'd do that.. then look at this: (x & (x - 1)) == 0 && x != 0
It's tricky the first time you see it, I suppose, but once you get used to it it's just so much simpler than any alternative that doesn't use bitmath. It works because subtracting 1 from a number means that the borrow starts at the rightmost end of the number and runs through all the zeroes, then stops at the first 1 which turns into a zero. ANDing that number with the original then makes the rightmost 1 zero. Powers of two only have one 1, which disappears, leaving zero. All other numbers will have at least one 1 left, except zero, which is a special case. A common variant doesn't test for zero, and is OK with treating it as power of two or knows that zero can't happen.
Similarly there are other things that you can easily do with bitmath, but not so easy without. As they say, use the right tool for the job. Sometimes bitmath is the right tool.