I gained most of that land in western Europe by pressing my vassals' claims for the kingdoms of England and Castille. I didn't actually try to engineer any of those claims for my vassals, so I was merely taking advantage of the opportunities that were already there. The reason I control French lands without actually fighting France is two fold. 1) England still controlled northern France because of the Norman conquest. Once I pressed my vassal's claim for England, Normandy naturally came with it. 2) Castille was somehow able to inherit the entire throne of France. They later lost control of the actual title but still retained a significant portion of the western French lands. Pressing my vassal's claim for Castille therefore brought Aquitaine into my empire, in addition to the Spanish lands. The Duchy of Gascogne actually came separately. I conquered it by pressing a dynasty member's claim. Though not a direct vassal, the dynastic affiliation is good enough to bring his lands within my realm.
Note, however, that in the case of England and Castille, I was pressing king-level titles. Since I was an emperor, I become their liege. If I was merely a king, they would become independent. Also, characters who are not part of your dynasty have to own land within your realm, or else they'll also become independent when you press their claim.
EDIT: I think the most impressive thing about that screenshot, rather than anything I did, was Norway forming Scandinavia. I've never seen the AI create an empire before.