Well, he did draw 2p on his turn 4. So there was definitely some luck in that. Oh AND his opening silver (and a copper) missed the reshuffle, being drawn turn 5; his opening was 3, 4, 4, 2p, 4p. By contrast, yours was 4,3,6,3,6. By the time he got his first familiar, you'd already gotten two $6 hands.
Based on the results, I suspect that skipping familiars was the wrong move - you won 30-25, not a big lead, and that's with 1st player advantage AND your opponent having some unlucky draws early. I would have expected that in this setup, all the cards you need are a little too expensive to go the route of 'skip cursing, just trash' - the trading post and lab are 5, border village/nobles are 6. Warehouse is pretty cheap though, I guess the warehouses can make it work, and you got draws which were on the nice side compared to his.