Only interactive shells read a file that may contain alias definitions. If you want to use a nickname for a command in shell snippets executed by applications, an alias is not the right tool. Instead, write a wrapper script like this:
#!/bin/sh
gvim --remote "$@"
Call it `~/bin/grim` and make it executable. Make sure you have `~/bin` in your `PATH` (you can put the script in any other directory that's in your `PATH`).
If you want it to work for every user on the system, put it in `/usr/local/bin` instead, ensuring that that directory is in everyone's PATH.