The idea here is not to transliterate (it's easy) but to have a keyboard that you can use without having Arabic key stickers. A mapping like this makes it easier to memorize the layout, because you can use English letters as a guide.

This strategy is also useful for other languages. For example, the regular Russian keyboard layout is "ЙЦУКЕН". It's completely phonetically different from "QWERTY", so if you can't touch-type, you'll need Russian keyboard stickers. But there's also a phonetic layout "ЯВЕРТЫ" which puts similarly sounding Russian letters onto the same keys as English letters.

This also exists for Arabic and other languages and has for maybe twenty years.

The first popular Arabic one was by a startup called Yamli. Google then launched a transliteration tool called Ta3reeb (I was working there at the time and helped build it during my 20% time). Microsoft then launched one called Maren.

They all let you type English letters then would try to deduce the Arabic words/script for it, and though the keyboard and mapping weren't exact, through some pretty primitive spell checks you could get 95% of the way there.

You're right, but: there's a one-to-one correspondence between some of these transliteration systems and the Arabic script (at least the Arabic script as used for Arabic, not for Arabic script as used for Urdu, western Punjabi, Pashto and other languages that use that script). And if you have a one-to-one correspondence, the keyboard can output Arabic letters as easily as Latin letters.