This is straight up misinformation.
The word "mosque" might have originally come from the Spanish, where they use the word "mezquita", which itself possibly came from transliterating Egyptian Arabic's hard g "masgid" instead of the soft j "masjid" you'd find in Classical Arabic.
(Fun fact: The vast majority of Spanish-speaking world has no vocal equivalent to Arabic's soft j.)
Meanwhile, the Spanish word for "mosquito" is, well, "mosquito" (which is derived from the Spanish word "mosca" meaning fly).
Some very basic Google searching suggests we got it from the French "mosquée" though. Which in turn probably came from the Italian "moschea" (although other possibilities include the Greek "masgidion"). Honestly, untangling which romantic language first came up with the word and which ones just borrowed from that is non-trivial.
To me, it ultimately seems unlikely that we took it from the Spanish at all, if only because the English language really has no problem with vowels like "e", or consonants like "z", or suffixes like "ita", so there would've been very little pressure for any of those to evolve "mezquita→mosque". Related comparison, the English word "mosquito" very likely did come from the Spanish word, and is practically unchanged.
Honestly, anyone who has studied linguistics to any degree would probably look at the text you quoted and roll their eyes. This sort of phonetic shift is incredibly common as words evolve, especially in loanwords between languages with different alphabets, and just because two words look similar in English doesn't mean they're in any way related. And the cases where any English word can point to one exact person or situation that actually spawned it are exceedingly rare. The fact that the quoted article presents it as if it's both clear and obvious is a huge red flag.