... by making a small but crucial tangent: package xbox games as standalone windows applications.
This simple adjustment to the trajectory of the xbox would have guaranteed dominance for Microsoft in both the console and PC markets. You can say that it would be a nightmare to patch xbox games so that they worked with the multitude of PC configurations in the wild - but Microsoft could have easily released a spec sheet and required certification for an "xbox ready" PC that must be adhered to in order to run xbox/xbox360 games. Think of the possibilities over the following 12 years: over time, we would not only have branded PCs that would run console games in addition to PC titles, but even laptops that are "xbox ready".
That could have been followed up by a digital distribution service for these PCs which would eventually trickle down to xbox live. A console/PC wide service similar to Steam perhaps?
I'm actually glad the xbox team felt they needed to act like a separate company from Microsoft, that kind of world domination would have been depressing!