In business the right course is often not obvious, and the merits of different approaches can be heavily debated.
In the case of the Xbox, Microsoft did both. It spent money developing the Xbox. It spent money investing in Windows. It also took lessons from the Xbox to make Windows itself a better gaming platform. And finally the cost of the Xbox approach was not as much as you'd think, because the division stood to recoup much of its costs.
How much did this cost Microsoft in the end? Less than you'd think, given the article. While it is true that costs were measured in billions and profits in millions, those costs were fixed development costs in the low billions, and profits recently have been quarterly profits in the hundreds of millions. I believe that at this point, over all generations of the Xbox, Microsoft is in the black. (But if they had invested their money differently, they could be further in the black.)
So what was the result in the end? I think they sliced something like a quarter off of Sony's profit margin. Almost for free. And Sony failed to execute on their strategy of having TVs replace PCs in the home.
Whatever you think of the merits of the strategy, Microsoft clearly thinks it works. They have used it repeatedly. For example look at Bing. And I wonder whether Google TV is an attempt to return the favor.