Yeah, the high score thing has got to be bogus. My wife and I like to compete to see who can get the highest score on Bejeweled's Butterflies mode. I finally had a pretty zen moment and hit almost 4 million. Then I decided to check out the high scores table and I'm to believe that four people have reached the apparent maximum score of 2,147,483,647. That's two billion points. That's either outright hacking or 4 very OCD people who spent hours if not days reaching that score.
Secondly, my first experience with asynchronous gameplay was a now defunct game called Duels. (Duels.com, but the website, which stayed up for a good year or more after the dev team abandoned the game seems to be gone for reals now). It was actually a really great game with a very loyal fanbase, but the devs inexplicably just dropped all support. The game itself was great. You had a "duelist" who you could send on click based quests to start. You earned gear which you could assign to slots and each class had special abilities.
Eventually you would have your duelist outfitted and send it to the arena to compete with other players. You'd challenge someone, set your loadout, pick ten actions for the round and then wait for your opponent to respond. Once they accepted, set their player up and clicked fight, the duel would play out. You'd come back, watch it play out and then move on to your next challenge.
Great fucking game. Unfortunately it really had a component of "get out the spread sheet and optimize" which was what you had to do if you wanted to top the leader boards, but it wasn't too bad. I think I eventually climbed to spot #24 before I started dropping again and then devs began withdrawing supports- bug fixes, ability nerfs and boosts, etc. - and then I kind of faded out. Checked back a few times to see if the promised support had ever returned, but it did not. Too bad, because as I said, it was a really well done game and the asynchronous play was a great model. I still miss it every now and then.