Those are slate tiles. The moss is hiding the raised edge of the tiles. They do overlap, of course.

Like this:

Who needs overlap when moss?

I'm gonna guess that they are slate or ceramic not wood.

And there is more than one layer.

Welcome to photos of houses in the EU that are not made of merely tape and lumber.

Whatever they are it looks like they need a good scraping

They're proper ceramic(?) / slate tiles and they do overlap but the moss may be hiding the joins.

With the kit I bought, very simple indeed. The sections clip together and are held spring-loaded in the gutters. Once I'd figured out the best way of fitting the sections together, it was a breeze.

https://www.screwfix.com/p/floplast-gutter-guards-black-100-115mm-x-500mm-10-pack/12515

The gutters had a thin plastic mesh covering them when we moved in, which had become brittle and fragile with age. This is a much more robust system and should work just as well (and last longer) than the previous installation. I guess we'll see in due course!

Thanks!