how is this a satire? (and other marx bros movies for that matter)

Maybe, maybe not. It could be argued that, of all the movies they made, "Duck Soup" is the truest satire, since it pokes fun at war and jingoistic nationalism and the very attitudes that started WWI and, six years after "Duck Soup's" release, WWII. The mindsets of Rufus T. Firefly and his flagwaving public (as well as his opponents from the rival nation) are not, at their core, so very different from the real world people and political leaders that, even today, rush headlong into senseless wars that end up costing billions and trillions of dollars, to say nothing of the immeasureable loss of human lives and human resources and commodities.

The "satire" in most of the Marx Brothers' other movies is in how they lampoon the conventions, fads and events of the real world that were contemporary with the times of their films' releases. Margaret DuMont, for instance, is ever the "grand society dame" Groucho flirts with in some half dozen Marx Brothers movies; what is it BUT satire when she endures, seemingly obliviously, his constant barrage of wisecracks and asides that ridicule the "pomp and circumstance" of the "blue-bloods," the "jet-setters" and the "priviledged class?"

But again, you are not far off in how you've sized it up. It IS a lot of silliness and nonsense. But it's satire, too. If the Marx Brothers knew one thing, it was to keep their audience laughing; satire is fine, and Groucho and company will indulge in THAT, too, but NOT at the expense of the laughs they can milk out of, say, Harpo's endless supply of scizzors, hammers, and other hardware that he'll pull out of his coat for any situation Harpo will deem fit to apply those tools!

Whatever you do, DO NOT read this sig--ACKKK!!! TOO LATE!!!

In this movie, the satire, which remains almost disturbingly current, is about college football and the lengths the heads of the colleges would go through to get decent players, putting it above the education they are supposed to provide. Duck Soup is about war and politics, with Grouchy as a greedy and immoral man put in charge of a country due to Dumont taking a shine to him. It wasn't as satirical in the MGM movies, at least not as overtly, but it was there. They parody then-current culture, hide dirty jokes where ever they could and attack every single character that might resemble an authority-figure.

Anyway, the most frequent target of the Marx Brothers' satire was the very idea of plot. A plot is presented, which the brothers procede to completely ignore, in favour of horsing around for 60 to 90 minutes. Sometimes someone pushes it along, in an attempt to get the movie back on track, but the Marx Brothers don't mind, they just don't care. Their movies don't end, they just sort of cut off, whenever the little plot left begins to peter out. They completely ignore the fourth wall and if they aren't harrasing a character with no relation to the plot, they are talking in circles with each other and everybody who might pass through their field of vision.