Are you kidding? Just because (1.) the US calls itself a democracy and (2.) many/most Americans believe it, it doesn't really mean very much. If the USA were a democracy similar to ancient Athens --- a "direct democracy" to use the technical term --- I would agree with you. But it isn't.
You said: "The nature of capitalist class society is that it is an economic dictatorship, not a political dictatorship."
Same thing if you ask me, since the enormous differences in access to the means of production --- i.e. class --- has to have profound implications for political process. How much is the average cost of campaign for the US Congress? I seem to recall a figure of $10mil being thrown around.....
"In other words it is the nature of a capitalist class society that, instead of standing over you with guns, the ruling class stands over you by monopolising the means of production and demanding you obey them or starve."
If it were that obvious it would not be happening would it? So maybe we're all very stupid. Or there are.....people with guns, stopping us from ending this state of affairs.
"The political state and the people with guns are under the democratic control of the people."
Really? I thought people with guns tended to follow their own rules.
"The capitalists don't directly control the people with guns (and don't usually need to), they control the purse-strings of the people who control the people with guns."
This doesn't sound very "democratic" to me.
"The US military (the people with the guns) are responsible to the the citizens of the US, collectively."
In theory yes; in practice, if (for example) the people don't even know the foreign policies enacted in their name, then there is absolutely no way that they can be responsible. Chomsky and others have demonstrated at length just how the flow of information is severely restricted and distorted in the US, compared to countries like (e.g.) Belgium and Australia.
"They get their orders from the politicians freely elected by Americans."
Voting according to what they know, which is not that much.
"Not from self-appointed dictators."
No, from dictators appointed by capital; especially capital in the strategic forms of laissez faire campaign funding and private/corporate media.
In fact, I don't think American democracy has really changed much since Marx & Engels wrote: "the executive of the modern state is a committee for organising the common affairs of the bourgeoisie." It's interesting that Marx's vision of the "higher stage" of communist society included direct democracy; his vision did not include the present-day travesty called "representative democracy".
Regards,
Grant.