/etc/profile
is not evaluated when you run sudo ...
as far as I know and the problem with the symbolic link is the mvim
script; if you look at it, it has these lines:
# GUI mode, implies forking case "$name" in m*|g*|rm*|rg*) gui=true ;; esac
Since you started it with sudo vi
the name does not fullfil the criteria to launch in GUI mode.
You could simply replace those two lines with gui = true
to "force" GUI mode, but I am not sure what else this might break.