Agree it's a super little table - so simple but "just right".
Without seeing a closer shot of the grain, can't be sure, but my money would not be on elm, certainly not for the legs. Doesn't have the "partridge breast" effect that you get with elm, and given what a pig elm is regarding movement, would be surprised at the top being so thin and staying so flat.
Ash, possibly, chestnut, maybe??