They mean they want their fascist leadership to have the support of murderous racists who feel metaphorically suffocated and stifled by having the “others” they vilify in their communities.
If you mean Lebensraum, it was living space, not breathing room. Hitler wanted to expand, widen his geographic boundaries into territory that belonged to others, as @ragingloli says. Believing that the German people were a superior race, he thought they were entitled. And of course this idea played out in ways other than geographic.
I don’t know anything about the fictitious general, but the concept is not dead, even if it persists in different ways and on a smaller scale.