Gamepads don't work in some Unity games

**Game information**
Another Star, Fight the Dragon, Heart&Slash, Race the Sun, almost certainly many, many others

**Distribution name and version where applicable**
Xubuntu 18.04.3

**Flatpak info**
Flatpak 1.4.3
nvidia-435-21
default
host

**Problem description**
Some Unity games, I guess depending on if the version of Unity they use is old enough, don't respond to gamepad input at all. The funny thing is that you can often work around this by forcing Steam Play to be used on the title. :x

**Does this issue reproduce with native Steam**
The games read gamepad input fine on "native" Steam.

No repository files or tests are named. Start by reproducing the issue with one of the listed Unity games under Flatpak Steam on Xubuntu, then compare its gamepad behavior with native Steam and with Steam Play; done means gamepad input works without requiring Steam Play.

Written by the indexing model from the issue text.