Hi! :D
I just saw your comment, I tested it on some Linux versions via VM and it worked for me but.. I think I know what the problem is. My personal PC is on windows and I created the TileMakerDOT_Linux_Launcher.sh file on windows and I see it 's using CR LF type endings (so basically it ends lines with /r/n) and probably Debian is using LF endings (just /n).
So when Debian reads the very first line (#!/bin/bash), it sees the invisible Windows character and reads it as #!/bin/bash\r. Because a program named bash\r doesn't exist on their computer, Debian panics and throws a misleading No such file or directory error.
In conclusion, I just edited the .sh file and changed what I explained above and it should work now, hopefully.. please give it a try :D