Sorry you didn't get your item. Auctions are won by high bids, not good timing. And sniping can't save an auction from the highest bidder. Sniping does not "game" the system; it just reduces the incentives(aka bids) for overheated bidding.
His MAXIMUM bid, the one entered at 15.07:38, was at least $76.99, one increment above $76.54, the next lowest bid. His maximum might have been $500; we will never know. But at the point he entered it, it was one increment higher than the existing bid, so eBay displayed this and only this: The Sum of the Existing Bid + One Increment (an unpublished amount set by eBay) - and not a penny more. EBay never, ever shows more than "existing bid + one increment." And it will keep showing only that number. At the end of the auction, when AS entered your bid on your behalf, eBay searched its system and found out that "Him" had bid at least on increment higher than YOUR maximum, as entered by AS. Acting as his "proxy," eBay automatically entered a bid on his behalf, a bid which was - yawn - one increment higher than your maximum.
If this strikes you as unfair, it is because I'm not explaining it clearly. Investigate further, and you'll see it is a very fair system.
I don't know why his bid didn't show up on the post-auction bidders list. It may have been there earlier when he was still the leading bidder; maybe eBay posts a winner's winning bid and none of the lower bids on his/her behalf. Or there could be some other reason. The list doesn't really matter; the bottom line is that you were outbid at 15.07:38, but you had no way of knowing that.
AS is not a magic bullet or a "cheat." It's good to keep in mind that the main advantages of AS are the convenience and the fact that nobody knows that you are "in the action." Sniping results in fewer visible bids; fewer bids reflect less demand and therefore tend to keep prices down. If everybody sniped we'd have silent auctions and no bidding wars. That would be an improvement, I believe.
Tom