Good for Square Enix, not great for Microsoft
Despite Microsoft seeming happy with Rise of the Tomb Raider selling somewhere greater than one million units, that couldn't have been the performance it hoped for when shelling out big bucks to wrap up limited-time exclusivity. The relatively low number wasn't a disinterest in Tomb Raider, though; it looks to have been a disinterest in Tomb Raider on that particular platform.
Superdata, a research group, released its January 2016 digital sales report today, and that data suggests that Rise of the Tomb Raider fared significantly better on PC. According to the report, "[It] sold almost three times as many units than it did on console during its first month."
There are some extenuating circumstances in play. As the report acknowledges, the PC version of Rise of the Tomb Raider released at a time when the triple-A schedule was more calm. Simply, there was less competition when compared to the middle of November.
Specifically, Rise of the Tomb Raider on Xbox launched on the same day as Fallout 4, which seemed a rather curious (and ill-advised) decision. Superdata says this is partially to blame for the console version's soft sales, even though top Xbox employees insisted this wasn't a problem because they are "not direct competitors, per se." In hindsight, it probably was a problem.
A rough estimate puts Rise of the Tomb Raider's three month (and lifetime) sales somewhere around four million. Square Enix hasn't offered an opinion on whether this is considered "a success" or, more importantly, if it's profitable yet. If not, the game still hasn't come to PlayStation 4, but it's expected to later this year. When that happens, it should prove to be another nice boost for the sales stats.