In my view, Roth's interest in NY and the Rosatos was strictly defensive. Michael had been trying to horn in on his gaming interests ever since he returned from Sicily--even arranging to kill Moe Green, Roth's best friend. Roth thought it was either kill or be killed. But, NY under Pentangeli, Michael's underboss, was his muscle and his deterrent--without his NY muscle, Michael would have been just another legitimate casino operator in Nevada, fair game for real gangsters.

So, Roth needed to neutralize NY. By pushing the Rosatos' claims, Roth was setting up Pentangeli. If the Tahoe assassination attempt had succeeded, Pentangeli would have been blamed. He'd be on the run, and the Rosatos would take over the "olive oil business" as Roth's allies. When Tahoe failed, Roth went to Plan 2: lure Michael to Havana, get the $2 million, and have him whacked. As a runup, he had the Rosatos plan to kill Pentangeli, so that Michael's successors wouldn't be able to call on NY muscle to avenge him.

A question presents itself: why didn't Michael get suspicious of Roth pushing the Rosatos' claims when he had no obvious interest in NY Mob politics? I'm guessing it was greed. He was hot for Roth's Cuban properties. Roth probably mollified him: "Look, Michael, I owe the Rosatos a favor. Just go along--it'll be good for our deal."