It's not often that I have the chance to comment critically on Webster 1913, so you must forgive me for not passing up this opportunity.
Webster 1913 lists the etymology of casemate as being via French from the Italian casamatta,"prob. from casa house + matto, f. matta, mad, weak, feeble, dim. from the same source as E. -mate in checkmate."
This is all well and good, but an alternative, and much more likely etymology is now considered more reasonable - to wit, that the Italian word casamatta derives from Greek chasmata, "chasm, cleft".
I am sure that you will agree that this makes more sense, given the meaning of the word.