Oh, it's pretty clear to me. Forget the Transportation-specific portions of their web page, and look at the introductory page, and read between the lines:

"A stones throw away from the Eur District, next to the Grande Raccordo Anulare, exit Eur Magliana, and close to the new Rome’s exibition centre, the hotel is within easy reach of Fiumicino International Apt and city centre to which is directly connected by a free scheduled shuttle service.All the wonders of Rome are only a few minutes away."

Decoding: They mix driving instructions and how close everything is in the same sentence! So they really mean it's only close if you're driving! Then they say it's connected by the shuttle service, and never saying anything else about any other way of geting around. This is a big clue that that's all there is!

Compare to the Express Rome - San Giovani, which in their introductory page says: " Express by Holiday Inn Rome - San Giovanni! is located in a very convenient position, with railway station 'Rome Tuscolana' within 300 metres serving International Fiumicino Airport, subway stop 'Pontelungo' within 500 meters and bus stop n. 85 just a stone throw away the hotel to quickly and easily reach downtown area."

Decoding: I have to do research on hoow often and what hours the subway and train run, and where they go, but I can see they're walkable, so no need to rely on an iffy shuttle! (And there's even a bus option, but if you don't already know the Rome bus system, that could take longer to figure out than using the subway.)

The only other thing I've found that works for me on Priority Club's website, besides the introducory text, is not the Transportation page, but the What's Nearby page, then using the Business & Attraction FInder at the bottom and choosing "Subways & Train Stations" and
clicking Find. In most European cities that map shows subway and train stations graphically, and you can zoom in to see how walkable it looks (for example, on that map for this hotel, you see that as the crow flies, subway stop 'Villini' might also seem close, but there's something in the way between the hotel and there and so you have to detour a lot to get there so the walking distance would be way further than to 'Ponte Lungo'.