For reference, I also deal with another marketplace (US based) and, when I asked them about the VAT regulations, their answer was (verbatim): “we chose not to comply with the new regulations”. This means that they will not handle VAT, even if they should.
I asked the local taxman what my responsibilities are in this case, and he confirmed that I have none. My responsibility is to charge the correct VAT rate when they pay me (i.e. no VAT, since they are in the US), and what they do with the final clients is entirely up to them. I cannot force them to pay VAT, after all.