It looks like Chromebooks could be getting tablet mode window management at some point in the future as it was recently reported that a chromium commit over at the Chromium Gerrit repositories included plenty of references to a new way for tablet mode to handle and manage Android apps when being used. As of this writing the Chromium Gerrit has now been removed from the Chromium repositories, so it's not possible to currently check out any of the wording or the references that were made to such changes.
Though the removal of the commit may not mean the new window management for tablet mode on Chromebooks is disappearing, it could mean that the work surrounding it has been paused or maybe it simply means that the team behind the development just didn't want the information out there for the public to see. Whatever the case may be for now, it seems that at the very least the feature may be coming to Chromebooks and is just a matter of when and how far in the future.
While it's impossible to know right now how window management might work for Chromebooks using Android apps in tablet mode, developers are seemingly hard at work on figuring out how to allow Chromebooks to best switch between app windows when tablet mode is being operated. According to the details that were seen before the commit was taken down, references were made to split-screen apps, resizing the windows of open apps, and the animations that happen as a user switches between the apps that are open and currently running. It was also noted that the portion of this new change that was or is currently being worked on was the first part of the project, which might mean that this will be split up into at least two parts, and possibly more, which may suggest that window management for tablet mode is not something that Chromebook users can expect in the very near future. That being said, current Chromebook owners might be able to get by with knowing that this is at least being worked on, as having the best possible window management for apps in tablet mode could greatly increase the enjoyment of using Android apps on a Chromebook when in tablet mode.