I think one important price factor is that this is "only" a plasma containment experiment and will only run Helium and Hydrogen, not the Deuterium-Tritium-mixture needed for energy-generating fusion.

This means it generates way less neutron radiation, which in turn means less need for shielding and easier working conditions on and close to the machinery, avoids material degradation, ...

Also, if I understand German sources correctly the 370 million doesn't include wages of the people working there (maybe external construction contractors, but not the effort by MPI personnel). (EDIT: found a quote of ~1 billion EUR as cost for the entire project since 1995)