Yes and no. Conceptually it's just three nested loops. The fiddly part is unrolling the inner loop and swizzling the data layouts in such a way that the cores can be kept "fed" efficiently. This usually means breaking things up into cache-sized chunks along some axis.

It's easy enough that there's blog articles showing single developers getting within spitting distance of NVIDIA's highly optimised code. As in, 80-something-percent of the best available algorithms!

All NVIDIA did was "put the effort in", where the effort isn't some super clever algorithm implemented by a unique genius, but they simply made hundreds of variants of the matmul algorithm optimised for various scenarios. It's a kind of algorithmic brute force for eking out every last percentage point for every shape and size of input matrices on every GPU model and even for various SLI configurations.

From what I've seen, AMD has done... none of this.