Any business can theoretically be put out of business.
In the case of an extraordinarily popular business like PlayStation, taking them out would take a massive effort on so many fronts that it would take no less than a decade before you made progress. And even that 'progress' would require everything to go right for Xbox and everything to go wrong for PlayStation; which just isn't going to happen under the current leadership and staffing of both companies. The PS3, for as much uncertainty as it caused and for as big of a financial mess as it was at launch, couldn't even do it and ultimately ended up outselling the Xbox 360. To word that differently, the best selling Xbox was outsold by the worst selling PlayStation. That should tell you how difficult it is to go up against a successful business.
So what a company like Microsoft would need to do is spend a tremendous amount of resources to kill PlayStation's hardware business, PlayStation's development and publishing business, and PlayStation's online and digital business... and they would need to do this in every country that sells a PlayStation... and they would need to do this while going up against the parent company (Sony) that won't let their most profitable business go down without exploring every possible avenue to stay alive... and they would need to do this all the while hoping that one of those avenues isn't appealing to the government of Japan to intervene for the sake of 'protecting national interests' which is really just a "You scratch my back and I'll scratch yours", usually in the form of really creative accounting by paying more taxes.
Basically, it would be a suicide run on Microsoft's part. The amount of resources that they would have to give up to effectively become the only player in the videogame business would be so large -- significantly larger than $7.5B -- that it would probably make more business sense to pivot Xbox into something else entirely (e.g. a subscription service) instead of taking on and trying to eliminate one of the console makers. Microsoft would need to buy every major publisher and developer (aka companies that make a shitload of money through PlayStation) and then some. That's a pretty big investment for a company with finite resources.