I just tried your code with two changes. I dropped the lines for setting the background (since you didn't post the image) and added strInput$ to the setting of EditBox 4:
SetEditBoxText(4,strDisplay$+chr(10)+strInput$)
Running on Windows in both v1076 and v1088, everything worked perfectly.
Broadcasting from v1076 to a v1076 Player (on an Android 4.1.1 device), works fine.
Broadcasting from v1088 to a v1088 Player, same results, but the input pop up didn't appear and text entry was directly in the EditBoxes.
Broadcasting from v1076 to a v1088 Player (NOT recommended procedure, by the way), the input was not returned from the EditBoxes and the Player reported an error.
Since, after rereading your original post, I think you were doing the third case, that explains the problem.
Use the correct Player version for the AppGameKit IDE you are broadcasting from. Otherwise, there is not guarantee that anything will work properly.
Cheers,
Ancient Lady
AGK Community Tester and AppGameKit Master