There probably wouldn't be a single hegemon in the region.
I would see Khwarazmians taking over Mesopotamia, as Buyids did before them. They had a good rap before Mongols came in, and were powerful enough to assure their hold on Abassids.
They would have to deal with turkic peoples they allied them, against Kithans. Eastern Persia is going to be troubled quite a bit, and the political fragmentation of Khwarazmians isn't going to help.
I suppose that Abbasids Caliphes may want to take a stand, as while declining, they still managed to know some sort of authority revival, but I don't think they would have the means to resist Turco-Persian control. At best, you'd end with something akin to Papal States/HRE or France relationship.
Seljuks weren't in decline. They simply didn't existed anymore as a political entity in ME.
That said, the Sljuk-issued Sultanate of Rum chances are interesting (I've mentioned them
there, some posts ago). Basically, they could set up their presence on Eastern Anatolia and Caucasus.
Couldn't the Ottomans (or something like them) still rise to power?
They would be likely butterflied. I wouldn''t see a conquest of western Anatolia happening at the same time than IOTL, and Rum is still the best candidate for the next century at least, if it doesn't collapse under its own wheight.
Without Mongols conquests, the situation would be different enough at least for a distnct beylicats period, maybe for maintaining Rum.
As for Syria, Palestine and Egypt, I could see a maintained division, with both Ayyubids and Mameluks unable to really take on each other.
At best, you'll end with two states : Syria and Egypt. At worst, while Egypt standing on its own, a series of states in Syria and Palestine reminiscent of the post-Selukid takeover situation (probably many of them clientelised either by Khwarazmians in the name of Abassids, Mameluks or even Rum)