I think the origin here is similar to some other words in that a manufacturer or company has created/invented a specific word or spelling so that it can be trademarked. Trademark law doesn't allow you to trademark a standard English word, so if you want to make a product whose name can carry a trademark, you need to have a unique word or spelling.
Take this manufacturer's torque wrench:
D-TORQ WRENCH DX | Topeak
They spell the name of the wrench "Torq", thus they can now have a trademark on that name and then no other manufacturer can have or sell a "Torq" wrench.
In another example, In the cable TV market, the orignal Science Fiction channel called themselves "Sci-Fi". But that's a common enough English word/phrase that it could not carry a trademark. So they rebranded themselves as "Syfy" so that they could trademark it.
Nevertheless, the correct English word is "torque", and other variants have arisen from the creation/invention of similar words for these other purposes.