To nitpick a bit, Hyatt actually has zero properties in the Rome area. The 7 that show when searching on hyatt.com are actually Small Luxury Hotels of the World (SLH) properties. SLH and Hyatt have a marketing arrangement, where one can book via hyatt.com for some limited benefits and often at a significant premium over booking the property directly.
Point taken, and actually makes the numbers look better for Marriott.
Still, for the purposes of OP's question, since they're bookable via Hyatt's site, and as you said, include some benefits, they at least reflect some "point" to that particular loyalty program-similar to the Design Hotels that show up when searching via Marriott.com.