Typically, I define the Weird West genre to be movies that take place in the Wild West and include some supernatural element. This usually means some sort of horror element like vampires or zombies, but that isn't really a requirement. So a movie with cowboys and dinosaurs fits my definition, even though it isn't really what I picture when I think of Weird West.
Yes, it has legendary Ray Harryhausen's stop-motion action, but the whole movie just seems silly to me. I don't know, I guess I'd call this one "Weird West, but I don't care to watch it".
Here's a trailer. I don't think it's streaming anywhere right now though.
I remember watching old Gene Autry episodes or movies on pbs on Sunday mornings and there being some wild stuff in them. I was young (5 or 6) so I do not have specific memories, but I do remember thinking this is weird.