There is trading activity in the milliseconds-seconds horizon as well. I'm sure all the big HFT players participate plenty. These just wouldn't be considered MM strategies.

Your original question was why MMs have to operate at HFT horizons. MMs by definition are liquidity providers (which means high availability and high volume at competitive prices). In some cases (DMMs) they're legally obligated to do so at some well defined baseline. And in that specific context HFT speeds are required.

To me, MM is the activity of providing liquidity with passive buy and sell orders - profiting from the spread while taking on inventory risk. That's also how exchanges define it, paying (or giving discounts to) traders whose orders are filled passively - the whole maker/taker incentive that was invented to attract customers a few decades ago. And we had human market makers well before electronic markets, and we still have them for illiquid markets today. They are (still now) called Market Makers even though they trade on minute scales!

So why is it not considered Market Making if I make decisions on millisecond or second scales? I don't understand how that is related to time horizon. So that's what I meant with original question, why can't I be a profitable market maker without HFT speeds? I still don't see the reason... Or are we just arguing about definitions here? Maybe when you say MM, what you really mean is HFT, but in my head the taxonomy looks completely different.

DMMs are a different story since that's basically just an SLA you have to adhere to, but not talking about DMMs in this case.

Slow market making is still market making, although rarely a good idea in my view. There are instruments with market makers operating at millisecond time scales. Not nearly as many as a few years ago, but they do still exist.