Google is testing Android 7.1 Nougat for Chrome OS in the Canary Channel, which suggests that they could be looking to introduce Android apps on Android 7.1 for Chrome OS in a near future update to the software. Since this is just in testing, and by the looks of it it's only in testing for a very select few, there's no way of knowing how long it might be before Google decides to open the capability up to more Chromebook users, but it's entirely possible that Google could have plans to bring this version of Android app support on Chrome OS forward with a near future version.
At the moment the Canary Channel is running on version 57, so it's being speculated that once Google releases Chrome OS 56 that Play Store support on Chromebooks will be based on Android 7.1.1 Nougat. Right now this is just speculation with no way to confirm a date for the potential release, but it has been confirmed to be in testing so Android Nougat is making its way to Chrome OS, and will eventually be available to more Chromebooks and more users.
According to the report, the Chromebook which had the Play Store running on Android 7.1.1 was a Lenovo ThinkPad Chromebook, so this particular model of Chromebook could be the only current laptop model that's compatible with Android 7.1 Nougat on the Canary Channel. Once Nougat for the Play Store is available on Chrome OS, users can expect new features to be available, such as the window resizing option, which is stated to be functioning decently although it is also mentioned that Nougat itself as a whole is showing significant signs of bugs, but this should come as no surprise as the Canary Channel is experimental. Once this version of the Android apps for Chrome OS passes though the developer and beta channels, the stability should increase with users being able to experience less issues. With testing being limited there is no clear indication at this point of which Chromebooks will see the compatibility first, but chances are that it would move through the Chromebook models that already have Play Store access in the beta channel before hitting other Chromebooks that are still waiting on Android app support.