To me it has more of a Sagrada Família vibe than medieval castle
We’re so used to shipping pine boards from the Pacific Northwest to the high desert we don’t even stop to consider there may be another option.
Fun fact: concrete is so heavy and so time dependent that it’s one of the few things that is still almost always VERY local; you probably have a home of cement mixers closer than you think!
Building very slowly can alert you to issues there, but they didn't always catch them (Pisa for example).
Typically named after (often Victorian) idle playboy who built them, and often with no attempt made to conceal their origins; they are only as "medieval" as the tastes of the playboy ran (so, more Tennyson than Terry Jones).
Reading through that website is...a trip.