Google hasn't said anything specific on how it plans to do the crossplay support except that it would require a Googlemade app to be installed on one's PC.
However, according to users who are able to try it out, there's no such requirement. A "Download on Windows" button appeared on the desktop version of Google Play for some and clicking on it downloads an executable file for Windows.
In any case, the chances are that you don't have that extra button on your Google Play store as the initial beta rollout is supposedly limited to South Korea, Hong Kong and Taiwan but users outside of those regions say they can try it out as well. So while it's a bit unclear at the moment, the development process seems to be moving quickly and you'll soon be able to play your favorite Android and PC games. Google has already asked game developers to optimize their games for non-touch keyboards and mice.