Depends on what you call an algorithm, of course. As GP mentioned bare minimum coding skills, I assume he uses really simple ones. This can, of course be relative, but maybe he was intentional with the analogy.

Because you can't really code without writing algorithms. Yes, you are never write a quick sort or implement a red-black tree, but you do have to understand problems and provide some kind of solution to them and then translate that into code. I.e. come up with an algorithm.

I used to use two simple problems, both involved math. One of them is a bit harder and the ideal solution assumes that you do remember high school math (not very complicated but something that you may have forgotten or at least something that you won't think should be used there). But it's nice, because you can come up with more and more optimal solutions and the naive one (which is O(n^2), IIRC, really just shows that you managed to understand the problem). I don't use that one anymore though. I almost exclusively just use the one that I thought was embarrassingly simple and which I used to use as a "warm up" exercise. Not more complicated than the fizz-buzz (which I hadn't heard of at the time I picked this one).

I'm not telling you here what it is, but it indeed does weed out people who can't really think through a simple problem and then can't think of a solution that consists of several steps following each other. (I.e. an algorithm.)

Now I'm not interviewing 'top' developers, just your average web devs most of the time. Another thing I'm doing in the past few years is code review. I have 2-3 pieces of badly written code that I have reviewed and/or rewritten.