There's some truth to it, but he sets up a false dichotomy between the 5 million members of the NRA (assumed to be against gun control) vs everybody else who is assumed to be for gun control. In fact, you have 5 million NRA members plus a bunch of freeloaders against gun control vs a large number of people who are for gun control, and an indeterminate number (I suspect the vast majority) who don't care.
His "cleaning up after a party" principle is called the Tragedy of the Commons -- but it works against *both* organized group.
The NRA is effective because it represents a large voting block (5MM plus the freeloaders minus the loyal Democrats) That's pretty much it. The 2nd Amendment probably also plays a part, but not the part you would expect -- it's because 2A shows the righteousness of the NRA's position and some politicians still have a somewhat working (although atrophied) conscience.