Just like the Google Chromecast, the Apple TV is unfortunately not suited for playing Slimme Playr content either. The problem is that Apple has not enabled this device to run a web browser. Since Slimme Playr uses regular web technology, this also prevents a Slimme Playr channel from being played on an Apple TV.
It's not a big loss that the Apple TV cannot play a Slimme Playr channel, since an Apple TV lies in a price range in which there actually are some good alternatives available, whereas e.g. the Chromecast is a lot cheaper.