No, these aren't practical algorithms. No one uses them in reality.
The hope is that these small improvements will lead to new insights that will then lead to big improvements. I doubt how matrix multiplication will be done will really change regardless of these theoretical results, unless something really groundbreaking and shocking is discovered.
It's all relatively pretty in the grand scheme of things.
I think the last thing I saw on matrices was looking toward optimizing slightly larger sub-problems.
That smells a little bit like a loop unrolling and/or locality improvement to me, You can often beat a theoretical algorithmic improvement with a practical one in such situations. And if you do a little bit of both you hopefully end up with something that's faster than the current most practical implementation.
The hope is that these small improvements will lead to new insights that will then lead to big improvements. I doubt how matrix multiplication will be done will really change regardless of these theoretical results, unless something really groundbreaking and shocking is discovered.
It's all relatively pretty in the grand scheme of things.