I can agree that Satan doesn't see God as a good ruler as stated at Gen 3:1-5. He doesn't seem to see Gods laws as right or good. But whether there is an understanding/agreement between God and Satan afterward to the effect that he can take the mantle of rulership to show whether his style is best is doubtful.
That conclusion is probably reached because God hasn't destroyed Satan, and he is also called the ruler of the world in the bible. So the thought goes that he is left to live because there is an ongoing issue.
I will rather think that Satan is still living because God doesn't always execute judgment immediately.
Satan ruling the world is not that he has absolute control of what goes on in the world. He rules the world of unfaithful mankind simply because those persons have chosen to disobey God's directions and laws. Any who obstinately disobey God is not reckoned as under God's rulership, as such to the opposing side, Satan. Before their destruction, Satan has authority over these persons since they wish to do things contrary to God's will. Since God's judgment doesn't come immediately, Satan just have a field day.
However, God is still in charge, and can hold them responsible for what they do any day, any time He decides. There is no prove-me-wrong senario here.
If there is any prove-me-wrong senario, I don't think God would immediately pass a death sentence on Satan in Eden. Gen 3:15. What will be the need for the contest when your fellow contestant is already been judged to be a loser and will be killed? If there is any contest, God won't destroy people with deluge and Sodom with fire and then the contest is still ongoing.
I mean why kill persons who are obviously enjoying Satan's rulership? Did the majority say that they were tired of the world they lived in or they were tired of the way they lived their lives? God didn't destroy them because they were tired of their lifestyle, but because their sin was too much for God to bear. It is true that there were outcry against Sodom, but probably Lot and few others had that perception, but not the majority in Sodom. So it appears that what is termed good rulership is what God sees as good, not necessarily what Satan or his followers see as good. If that is the case, there is no contest here.
If you think about it, majority still see God's standard as too restrictive and bad for them. They rather prefer independence as the best option. Will that make Satan a winner of the contest? If not, what will? I don't think that majority will one day want God's rulership. But God will still destroy them if they don't choose to obey HIM. So God is and will always be the ruler. That He allows bad people to stay temporarily doesn't mean that He wants to prove anything, but He is loving, patient, doesn't quickly execute judgment because we're free moral agents.
We are created to make our own decisions, God won't always let those who disobey Him to live. He will destroy them, but He doesn't do so immediately. That time lag makes the wicked and Satan to cause problem for the just.
We don't want to forget the fact that God was the ruler of the kingdom of Israel. This is obviously because Abraham accepted to follow His laws. There came his descendants. For God to rule Israel is a bridge of contract if the issue of Eden is true. God even intervened and appointed some kings in another lands like Syria. At Dan 5;21 he stated that He has authority to appoint and remove kings and that He is the king in the kingdom of mankind. That would have been a brigde of contract. He calls all kings as being his ministers as well.
However, since these kings might chose to disobey God and even worship demons, God normally let them be and Satan will control them. That doesn't mean that if God wants to intervene in those rulership He wouldn't. He is always in charge.