I saw your post a few days ago and went to look at the app page at the Google Play Store. I wanted to see if it shows landscape in any of the screenshots and it doesn't. Usually developers will show various screens, screenshots and orientations in the app description. I use Google Messages but only on my phone so I couldn't really test your situation, but on my phone it doesn't display in landscape either.
My only advice would be to check that your tab's option to auto rotate is enabled. You might also check the settings for the tablet version of the app to see if there is a setting for it.