Market makers need to be able to close arbitrage opportunities or they won't participate in the market. Speed matters just as much to them as it does to the prop traders.
Of course market makers wouldn't want to compete in a market where they are forced to make much slower trades than anyone else. But market making existed long before HFT, so it can't possibly be a unique benefit of it. You can argue that market making has become better because of HFT, but not that it requires HFT.
The technical aspects are more cross-cutting than your labels. "HFT" is for the most part just a latency threshold being crossed, whereas more functional roles such as market making, various forms of "pure" arbitrage, statistical arbitrage, prop trading, etc. have existed at the older latencies as well as the newer. All participants benefit from having lower-latency access than their competition, which creates a (thus far) neverending arms-race as firms leapfrog each other.