Monker is right.

The vote count for the name rights to Styx went to the guys calling themselves Styx. Whatever they perform as Styx, and whoever ends up in the band to perform it, they legitimately hold the name.
So, I ask, why put in a Damn Yankees song? Or any Gowan song? Stick to the enormous Styx catalog. There are plenty in there that would suit this lineup perfectly. Maybe they better start throwing in the new song. Or "Sing for the Day" to promote this new release of theirs. I don't get "High Enough" being in the set at all. You are Styx. Sing Styx songs. Preferably ones that Gowan isn't featured prominently on, though. (JMO)
Dennis, on the other hand, is basically billing himself as someone performing the "music of Styx". He can throw in anything he likes. And can bring in players to do songs from the Styx catalog if he wants. He is not calling his band "Styx."
That said, I agree with Boomchild. I am none too happy about the addition of the Shaw-penned songs to DDY's show, since I think he took out some terrific Styx songs and solo songs he wrote to put those others in. But I do see WHY he is doing it, as has been discussed in a couple of other threads here awhile back. He is putting out a more well-rounded presentation of Styx music, plus he gets some voice rest during the set.
Bugsy