#15 28 by the way vs at the way, on the way
Sorry. I got it already
Another question
devoted/requested/claimed/dedicated

The island was known (25)____to_________ the Spanish but still uninhabited in 1609, when Sir George Somers ran aground on a sandbank in a storm and (26)____devoted/requested/claimed/dedicated__ it for the Crown. The "pretty" town of St George's, which he founded, is the oldest English (27)____community______ in the New World.

P.S.: The key says 'claimed' however, I still can't get the whole situation.

Question

#15 28 by the way vs at the way, on the way
Sorry. I got it already
Another question 
devoted/requested/claimed/dedicated

The island was known (25)____to_________ the Spanish but still uninhabited in 1609, when Sir George Somers ran aground on a sandbank in a storm and (26)____devoted/requested/claimed/dedicated__ it for the Crown. The "pretty" town of St George's, which he founded, is the oldest English (27)____community______ in the New World.

P.S.: The key says 'claimed' however, I still can't get the whole situation.

Answer

The answer is "claimed". 
He officially announced (to the world) that this place now belonged to the king. 
He was acting in the place of/ on behalf of the king - as the king's (or "the Crown's") representative.