Complex sentence: Their ideas were a challenge to the existing orthodoxy popularised by the German Siegbert Tarrasch which was a rather dogmatic distillation of the ideas worked out by the great chess pioneer Wilhelm Steinitz.
Split into simpler sentences: Their ideas were a thus challenge to the existing orthodoxy popularised by Tarrasch. This orthodoxy was a rather dogmatic distillation of the ideas worked out by the great chess pioneer Wilhelm Steinitz.