Building an engine against IGGs isn't always terrible, since the IGG player can't end the game that fast on his own. He needs to hit $5 18 times to do so. So you have a fair number of turns. Of course, if you're not attacking him, hitting $5 18 times doesn't really take that long, and trying to build an engine with constant Curses streaming into your deck isn't the fastest thing in the world.
Now in this particular kingdom there are attacks, but there's also Lighthouse. So on all the non-$5 turns, the IGG player is taking Lighthouses, and you're not going to have the easiest time in the world attacking him. Additionally, the only trashing you can get is Trade Route, and the only cycling is Minion, which can run into rough times if you have too much junk in your deck, since it's just blind-drawing 4-card hands. Still if your only goal is to play as many Unis as possible and land on a Potion to buy a Vineyard there is some hope. I'd lean toward IGG, though.