How to trick a program into thinking there is no X server running

If you want to disable X for a single command you can write

DISPLAY= ./my_command

Notice the strategical blank space after =. More generally, you can set environment variables for a process by prefixing your command with a sequence of <variable>=<value> separated by spaces. Since space serves as separator, = immediately followed by a space clears the preceding variable. We can look at the effect of these prefixes by using a subshell as the command and then printing its environment. Take for instance:

$ A=a B=b C= D=d sh
$ echo $A $B $C $D

This will print

a b d

This shows that the environment of the subshell indeed is different as intended. Note that shell substitution happens before the individual arguments are passed to echo. This means that echo will be called with three arguments and so there's only a single space between b and d in the output, just as if the command line were echo a b d (even though there are two spaces before d it only prints single spaces), but unlike echo a b "" d (which prints two spaces between b and d).