Enschede is serviced by German rail operators though, so that might be a reason. In fact a lot of trains in this region of the world are operated by neighboring countries ..

> Enschede is serviced by German rail operators though

Yes, there is a train service to Germany, but the majority of the connections from Enschede are to/from the Netherlands.

> In fact a lot of trains in this region of the world are operated by neighboring countries

If a service to Germany causes the whole station to be labeled as German, the website might just as well label Berlin as Czech, or Brussels as Dutch: CZ (Czech national railway) has train services that extend to at least Berlin, and NS (Dutch national railway) has trains to Brussels.