My guess is that the whole assembly isn't FCC certified, though not necessarily non-compliant - since they weren't intended for the US market. The modem (for sure) won't work in the US, though it doesn't seem to harm either the modem or the network. The power supply and CRT are CE certified, which is as stringent, if not moreso, than UL certification. It's a safe design if used as-is.
The only other bits of interest are the network and USB ports, which are part of a standard Intel mainboard - and which IS FCC certified. (the dot.station uses a standard Intel D810EMO/MO810E mainboard assembly - though they typically used the i810 chipset instead of the i810e) Most boards still have the FCC sticker on them - so I suspect they are applied at the factory. Like most consumer electronics, it has multiple certifications because the board was sold in a lot of markets, including the US.
I'd say as long as you remove or abandon the modem, you should be good to go. BTW - even if your dot.station DOES cause a problem, you aren't necessarily off (or on) the hook because it was UL listed or FCC approved. You can still be sued if your UL listed coffee maker burns down an apartment complex, and the FCC can still jump you if your FCC certified mainboard causes problems for the HAM operator down the road. (check out the part B certification on most electronics - you are STILL responsible for correcting the problem if it generates too much noise)
Basically, the machine isn't going to burn down your house, and it is actually more RF clean than a lot of standard PC's. I wouldn't worry about it too much.