Air hose size has a lot to do with CFM! If it's an air powered angle grinder, they take a lot of CFM. A 7" air grinder will need a 1/2" or larger air line to get enough CFM. It's no different than a water hose. Say you have a 4" pump that puts out 750 GPM but you only have a 2" hose. There's no way a 2" hose will flow 750 GPM. A 3/8" hose may flow enough CFM but it depends on how much the grinder needs and the output of the compressor.
As to the original question, the compressor in question falls into a grey area as it is not a true 6 1/2 HP motor. It's probably closer to a 1 HP especially if it runs on 115 volts or maybe 2 HP on 230 volts. It it was a 7 1/2 HP would make more sense because they actually make a true 7 1/2 HP motor but it is about 3 times bigger than the fake 6 1/2 HP and would cost about 3 times as much as the whole compressor just for motor alone. I suspect the compressor may be too small to run the grinder once the reserve capacity in the tank is used up. Just like using a big impact wrench, it's good for a few minutes but then the compressor alone won't keep up.