It is all very simple. His bid was already the high bid when your snipe came in, but the amount shown prior to your bid arriving was only the amount of the second place bid at THAT TIME plus one increment.
When your snipe came in at the last second, a larger amount of his proxy bid was revealed, enough to equal YOUR bid plus one increment. As was stated, his maximum bid amount may have been much higher. The amount shown is only the amount of the second highest bid plus one increment.
All of us had to understand this when we first started on eBay. This same question is asked here quite frequently by folks new to eBay. You will want to read up on proxy bidding, using eBay's help section. It is very important that you understand how proxy bidding works, if you are to use eBay and also if you snipe here. Good luck.