I am the author.
> The first mistake the developer made, was that he wanted to create a different user experience between keyboard and mouse. Stick to what you get by default and design your components so they work for both usecases.
We have. The behaviour is mostly the same whether you're using the keyboard or a pointer (mouse/touch/pen). The only difference is that, for keyboard users, we want to turn off the animation and move the focus to the first link in the menu instead of focussing on the menu's parent <ul>.
The problem was that, as various devs have iterated on the menu over the years, it's broken the fallback behaviour. For my colleague on the funny multi-monitor set up, it should have fallen back to the keyboard no-animation behaviour with no real major difference to the UX, but instead it fell back to the no-JS experience.
So yes, generally don't try to be smart with accessibility, avoid ARIA attributes except where necessary, etc, but click events are the universal input event and work on any kind of input device and have perfect browser support. It's far better for accessibility using them instead of a mix of keydown and mousedown or pointerdown, and potentially missing other kinds of input events.
As I stated in another comment, if it was a scenario where there needs to be a major difference in behaviour between keyboard and pointers, then I would rather use separate keydown and pointerdown events.