You've gotten some good responses here! I would also chime in with trying hard to catch when he is arguing instead of obeying, as that is non-negotiable in my book, and I'm sure yours as well! He's smart, so when it's not an issue of obeying, could you challenge him to prove what he's talking about? Like with the checkers, get out the rules and read them. Perhaps before playing a game agree that playing a game means following the rules, and if he doesn't want to follow the rules, then put the game up (as you did), but no arguing allowed. And, he may be too young for this, but perhaps there will be opportunities to teach the difference between a fact and an opinion? Facts are not up for arguing, and opinions are to be shared, not forced on everyone else.
Just some thoughts!
Laura
p.s. I would like to add that in our house, respect is of the utmost importance. It is required that we get a respectful answer first, be that "yes mom", or whatever, and then they may ask a question or express an opinion ("may I finish this first?") Truly, if you aren't getting obedience from him, then that is where you must start, and I would suggest you let him know things are going to be different, and then hang on as he will no doubt try you for a time to see if you are serious.