Is this 230V steampunk metal robot lamp safe?
It's dangerous.  You've spotted one important flaw but it can combine with others to make a really dangerous product.
I originally suspected it was made in Europe by someone with more interest/knowledge in the sculptural aspect than the electrical one, but I've since spotted contact details in China for the seller. Either way it shouldn't be sold.
Here's why (as I only have a little training in designing stuff for mains, and haven't inspected it, this list isn't exhaustive):

It needs be earthed (assuming the metal really is metal and not plastic).
Wire nuts are rare in Europe and any decent solution shouldn't need tape.
Secondary securing on the wires near the joints is a good idea, even required in some cases but needs to be much more solid than tape.
I doubt the wire is properly strain-relieved where it goes into the assembly. This is now confirmed by the 4th picture. The wire nuts will take the strain of any pull on the cable, and the edges of the cable hole can abrade the insulation.

This adds up to a dangerous and easily foreseeable failure mode where you trip over the cable, rip the live out of the wire nut, it touches the pipes, making them live, you pick up the lamp, you wake up in hospital - if you're lucky.
I've been known to cut corners for something I'm using myself, but not to anything like this extent, and certainly not for something that's going to be used by others.
These days the preferred solution would be an external low voltage power supply (complying with the regulations and safe on the output), but it could be built safely for mains operation - it just hasn't been.