This style is usually played with a voice that resembles a Hammond B3 with percussion. A Leslie speaker (effect) adds a lot if it is tastefully used.
This is played in a choppy two handed staccato style. I found video that has this style of playing, albeit very little of it. Watch the keyboard player in the rear on a riser and wearing a red shirt. You'll only rarely get a good shot of him. This is Kevin Adamson. I've only seen a few organ players employ this playing style. IMHO many keyboard players overplay, they tend to muddy up an arrangement. But this style can be played nice and "sparse".