Not all of them, surely? There must be at least some false gods who have no existence at all, I would have thought. I remember quotes suggesting they exist but none which say they all do, or ones which identify the existing-but-fake ones from the entirely nonexistant ones. Zeus could be entirely nonexistant.
RT I’m pretty certain that Zeus was ‘animated’ by some satanic being, but I sort of agree with 'not all false gods are demons/fallen angels. Satan is not omni-present but seems to have plenty of forces in some sort of power structure on the earth and heavens. If you start worshiping your left shoe as ‘god’ there is a (IMHO) good chance that it will go un observed by satanic forces. The more you worship your left shoe the greater the chance that it will be observed, the more people you involve in your shoe worship the greater chance one of them may bring a demon with them, or state your shoe-religion to others in earshot of the enemy.
Once the enemy knows about your shoe worship that object can have a demon/fallen angel behind it, empowered by the curse you incurred by worshiping a left shoe before God.
Hey, i’ve got to worry about my Immortal Sole, don’t I? 
Assuming all this is correct, one could presume that all false gods claim to be true gods, and play the role as well to the best of their ability.
That is, that all false gods say exactly thing as your god says to you, give or take irrelevencies such as whether to sprinkle or dunk and the like.
I dub the argument that all other gods are real, but “false”, and that the speaker’s god is “true”, based on the evidence in the “true” god’s words and writings, I dub this the “No True Godsman” fallacy.
(“Zeus’s followers don’t count because none of them are a true God’s man! Only I and people who believe like me are a true God’s man!”)
Kanicbird to repeat one of my previous questions (albeit spell checked this time) how do you tell the difference between faith in a real deity and faith in a false deity? Hopefully there’s a more objective answer than “If it’s faith in my God, it’s real. Otherwise it’s false.”
God is interactive with us, it does take time and faith to realize just how much. This at the least proves to me that He is a living entity. How He has lead me and how true He has been indicates His goodness. His command over the enemy has demonstrated His power.
But you’ve said that you believe that false gods are also living entities, so can’t they interact like God would? Presumedly they can also tell lies or twist the truth to suit themselves and we, as fallible mortals, might be convinced by their lies. And the idea that God is real because he conquers his enemies seems suspect to me: a theological version of might makes right.
Sort of, but not exactly.
I said that God’s command over the enemy demostrated His power (to me), not that He is real because He has that command over them.