It wasn't really in character for Alexander to accept this peace with Darius. We know that because obviously that's exactly what he did IOTL... plus all the other mountains of evidence as to what kind of personality Alexander had. However, that said, that reasoning can prevent discussion of a lot of alt history scenarios, so it seems kind of unreasonable to just say "nope, would never happen". It's not impossible, it just requires an Alexander with a different mindset. (edit: Son of Leman Russ has a good potential POD for changing Alex's mindset)
Anyways, I think the most beneficial change as far as the survival of the Argead empire goes is that Alexander probably looks to marry and father an heir - not that the subtraction of territory doesn't help a lot in that respect as well, but the Macedonian royal family was infamous for its long, bloody succession conflicts. As Mary Renault said, "the earlier history of Macedon makes it plain that his successors simply reverted to the ancestral pattern of tribal and familial struggles for the throne; except that Alexander had given them a world stage on which to do it." Now part of the terms that Darius offered were that Alexander would marry his daughter Stateira, whom Alexander would later marry IOTL. If the two have a son within a couple years, that not only simplifies the Argead succession, but it also gives the Argeads a stronger claim beyond right of conquest to rule the entire Persian Empire. I would think that later on down the road, when Alexander finally decides to finish the job (which I imagine he would), that this claim would come into affect, since he declined the use the right of conquest claim by accepting the terms in the first place.
As far as governing goes, Alexander probably maintains his OTL policy of maintaining the old Persian system except with Macedonians oftentimes usurping Persian satraps and officials. This had positives and negatives in real life, and would here too. He probably still founds his Alexandrias too, especially the one in Egypt. I'd imagine he'd be even more drawn to Egypt ITTL than he was IOTL. While he wouldn't do it right away, he might down the line consider setting up his court in Egypt.
As I brought up earlier, I still see it likely in this scenario that Alexander eventually conquers the rest of the Persian Empire. Or at the very least the Macedonians do under his son, if for whatever reason Alexander dies young and with the east unconquered ITTL. But doing it in stages like this should significantly help the stability of the empire, not only because it gives Alexander time to consolidate his rule over the very large conquered regions of Anatolia, Syria, and Egypt, but also because he should leave behind a much older son should he still die around the time he died IOTL - which by all likelihood he should live longer.