Let's start from the beginning. The Play, from a pure hardware view, can run ICS. Sony, HTC and other companies are releasing hardware with ICS and lower specs than the Play (Tapioca, Desire C). We've seen that the beta runs mighty fine in the performance department, and it's obvious that the job can be finished if Sony cares to do so.
However, this is a matter of the gaming ecosystem. In short: the only companies Sony cares about are the big names like EA, Gameloft, Rockstar, etc. as they make the big majority of the Play game sales.
However, with regard to development, the Play is not important to those big names: they see it as "the redheaded stepchild Android", because they have to make extra effort to make it work with the game pads, instead of easily deploying the code in it like they do in the whole different platforms they code for (not only mobile phones, but smart TV's, console-related app stores, Steam and so on). Sony bribed those big developers with a lot of cash (remember all those free EA games and temporary exclusives?) so that the Play remained visible.
Fast forward to now. Gingerbread is present in a good 60% of Android Play Store-running hardware. ICS has only like.a 4%. Android is the best selling platform, with, let's say 500 million active devices. If my numbers are not wrong, that gives 300M GB devices 20M ICS ones. Developing with ICS in mind implies higher development costs, because you have to study the new features and use them. And of course, big name developers target wide audiences: by default they'll program with Gingerbread in mind, so they couldn't care less about ICS right now.
Someone mentioned Windows 7 incompatibility with old games: there is actually a Compatibility mode which was mainly designed for the purpose of using older games. Now Steam has taken care of that, which suits MS fine.
With the ICS upgrade, Sony probably contacted their "partners" and asked them to update their software (basically switch from the Sony custom gamepad framework to Google's standard one which Sony probably contributed themselves) for it to work properly in ICS, like they do in Sony gaming platforms. But unlike the PlayStations, it's those big name developers who are in control now, particularly in Android. Therefore, they showed Sony the middle finger.
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TL;DR this is a power struggle between Sony and the big name game developers. The latter have won here, at the expense of the users. Support independent developers but make sure they don't make the "big name" status, because they'll get the need to control everything and screw users like this.
