Since you are accepting Answers about how this might be done, I'll convert my Comments to offer another viable suggestion.
First off take note that the main field of the tabletop appears to be a plywood panel, which allows for the outer frame and the attachment of a solid leg assembly without accommodation for wood movement as you probably should with any solid-wood top of these dimensions.
Although there appear to be no fasteners used, they could be there but hidden by wooden plugs or even filler. However this design can be built using only simple joinery and glue without too much difficulty.
My thought on the construction was that the legs may simply be glued into mortises in the tabletop frame, or alternatively have stub tenons formed on their ends. I don't think there's a good reason to prefer one over the other for a table of this kind, which must be treated with care and respect — this would not be a suitable choice for the busy living room of a family with boisterous kids!
Glueing the legs directly into shallow mortises might seem weak, and it would be weaker than we'd normally expect to see (although standards for that vary wildly with furniture type and level1), but joined to the gallery elements I could see this easily being strong enough for service in the type of home that would have a piece like this, especially as I imagine the 'rails' are mortised into all legs so the understructure can work together as a single unit.
Additionally, glueing the top rail of all four gallery elements is possible, and would add even more strength2.
1 What we might call 'art furniture' is sometimes built with looks first and structural integrity or outright strength second (or third or fourth!). Note that it's still common to see handmade furniture finished in shellac and wax, or just oiled, when factory stuff has nearly always had a lacquer or varnish finish for nearly 100 years now.
2 Remembering that glued long-grain surfaces like this are stronger than the wood itself.