Well, we could safely assume that a lot happened between the Bronze Age and 1100 A.D. Yet, I find it remarkable that the Cypriots would still cluster very close to the Bronze Age Anatolians. One might say, Cyprus, being an island was probably better isolated from migrations within Anatolia. The same is true, after all, for other Greek islanders. Yet, also people like Albanians are quite close to Bronze Age Anatolians. So in this regard, we have to assume that until 1100 A.D. there has been a larger genetic shift in Anatolia than there has been in the Balkans. Perhaps, but still, I find that hard to believe.
Instead, I think this may indeed have something to do with the fact that Anatolia was heterogenous and that these Bronze Age specimens are from Western Anatolians as Boreas stated. Makes sense, if Western Anatolia was somewhat Mycenaean-like during the Bronze Age, and the Cypriots were perhaps colonized by Anatolian like peoples and Mycenaeans, then the similarity makes sense. The Central and Eastern Anatolians had more Caucasus input. Turks brought even more of that. So, the difference between Western Bronze Age Anatolians and modern Turks is considerable.
That said, in this line of thought Western Turks should be Western Anatolians + some Turkish admixture. They should therefore cluster closer to the Bronze Age Western Anatolians. I.e. closer to modern Cypriots. I don't know whether this is true.