Error `No protocol specified` when running from remote machine via ssh

The meaning of the option -display 127.0.0.1:0.0 depends on that gui program, but it's highly likely that it means “display on the X display 127.0.0.1:0.0”. This is the first local X display, accessed over TCP. This is almost certainly wrong for two reasons. First, the local X display should be :0, not 127.0.0.1:0, because including an IP address causes the traffic to go through TCP instead of local access. Going through TCP may not work depending on whether the X server accepts TCP connections. Even if it does, you lose the optimizations that local displays have.

The display to use is normally indicated by the DISPLAY environment variable, and that variable tends to be set correctly automatically. (Usually, if DISPLAY has the wrong value, it's because you've been messing with it. The main exception is use of screen or tmux.)

Your program probably does look up the value of the DISPLAY environment variable, because that tends to happen automatically with xlib calls. So you should just call ./gui, your script doesn't do anything useful. If your program insists on the -display argument, make it use the environment variable:

./gui -display "$DISPLAY"

ssh -Y and ssh -X should be a good start but did you forward your X server as well?

$ grep X /etc/ssh/sshd_config
X11Forwarding yes

otherwise it won't work.

Another thing to check is the DISPLAY variable it should show something like this:

$ echo $DISPLAY
$ localhost:10.0

this was run after ssh -Y. The same variable is empty if I ssh without -Y or -X.

For differences between -X and -Y read the man page of ssh.