Android Keyboard Not Working with GameMaker on Chrome Remote Desktop

Question

I once programmed a simple PC game with GameMaker 8.1 and exported it as an .exe file. The game relies heavily on listening for the user's key presses. I want to be able to run the game on my PC, share the PC screen with my Android phone via Chrome Remote Desktop, and allow both devices to send keyboard input to the game.

I tried doing this and it almost worked. The problem I ran into was that for most keys, the Android phone's keyboard did not trigger any of GameMaker's key press events even though the PC's keyboard did. I tried switching between various keyboards installed on the phone, but they all had the same problem.

Interestingly, the Enter key did work in-game on the phone -- triggering the corresponding Enter-key-press event -- whereas none of the letter or number keys worked. Also, during the portions of the game when the user has to type inside a GameMaker dialog box, the entire phone keyboard worked for entering text.

I know this is a niche issue with an odd combination of software, but can anyone explain why this happens? And is there a fix besides rewriting the game code?