These ratings are the gasolines ability to resist detonating. Which basically means and uncontrolled explosion of the gasoline in the combustion chamber. If the knock is audible it can be and probably is causing internal engine damage.
The knock sensors that are installed on modern vehicles are going to "listen" for detonation. Which happens at a level way more sensitive than what a human could hear especially over the noise of a running engine. When they "hear" detonation they are going to retard the timing on the engine until the detonation goes away. Typically the ECU will try to advance the timing back to the normal level but if the detonation persists it will not. Retarding the timing does reduce the total available power output of the engine.
The higher the octane rating the more resistant the fuel is to detonation.
The current offering from BMW with the exception of a couple of holdovers are all turbocharged which is going to mean that the engines are much more prone to detonation and as such should be run on the highest octane readily available.
As stated 89 should be a minimum and I wouldn't use it regularly but only as a last ditch. Some states like California use 91 as their highest octane while most use 93. Use the highest readily available. Is my opinion.
Are you going to destroy your engine running 89 octane? Probably not. But depending on other factors such as ambiant temperature and load on the engine you may have enough detonation that the engine is drastically retarding the timing to protect itself and as such you are losing significant engine power in the process.
This is really not just a money grab. There is science and engineering behind this stuff. As the manufacturers continue to build higher horsepower engines while trying to maintain emissions and get higher efficiencies (read mpg) from their engines this will become more and more common. Remember the days of leaded fuel. Probably some of you don't. E85 or something like it may be the next answer, but until then do yourself a favor and use the highest octane fuel available in your new BMW.