It is not possible to play the game on the Nexus Player/Android TV. The app hasn't been marked as supporting Android TV so it doesn't appear in the Play Store. And since Android TV doesn't have a touchscreen, it wouldn't be possible to play the game even if it was side-loaded.
The original poster merely mentioned it because the game works on the Amazon FireTV with it's controller, which is almost identical to the Nexus Player's, so it should be extremely easily to implement support for.
Android TV will ultimately take off this year as more devices arrive so I have no doubt that Machinarium will be supported eventually. We'd just obviously rather be able to play it now.