M is of course just the Roman numeral for 1000. They did not use the Arabic system that is standard today. So MMII meant 1000 plus 1000 plus 1 plus 1 - that is 2002. If you want to talk mean about the Arabs, you better stop using their numbering system first.
For the use of “k”, you can blame the Greeks, but mainly the French.
In ancient Greek, the word for “thousand” is"chilioi". It starts wth the letter chi, a hard “ch” like in “school”. So it sounds like kilioi.
The French introduced the Metric system around 1795, after their Revolution, with new measures like grammes, metres and litres. BTW - the inventors spelt them that way. Americans are out of step in calling them grams, meters and liters.
To express multiples of the new measures, they used Greek prefixes. “Deka” in Greek was ten, so a decagramme was ten grammes. For a thousand of something, they used “kilo”. Strictly, it should have been “chilo”, but they were practical about it. So, a kilogramme was a thousand grammes.
People today rarely use prefixes other than “kilo” - grammes and kilogrammes, metres and kilometres. These are written as g and kg, m and km. So “k” has come to mean “a thousand of something being measured”.
This has been transferred to money. $100k was used for $100, 000. To be logical about it, we should have used the Roman M, but this would have been confusing, since it also means million and mile and metre and so on.
So, “k” has come to mean 1000.
QED - Quod erat demonstrandum, as we used to say in those old days in Rome. Ah, those were the days amicus meus.