The book was sincerely advocating
Was examining ideas. A lot of Heinlein's novels were like this.
Stranger in a Strange Land: the effects of organized religion on culture, cults, and free love.
The Moon is a Harsh Mistress: colonialism, libertarian ideals in extreme environments, polygamy, to some people telling a story from the perspective of a character with an intellectual disability.
I Will Fear No Evil: body dysphoria, the privilege of wealth, multiple personalities occupying the same body.
Starship Troopers was an examination of self-sacrificing behavior and civic responsibility.
for a democratic government where only soldiers were allowed to vote.
Only people who worked in public service for a set period of time. Soldiering was the profession focused on because Heinlein was interested specifically in self-sacrificing behavior, but it is explicitly laid out that
any government work qualifies a person for citizenship, regardless of whether they're a scientist, a pilot, or a janitor. If a person wants citizenship but is totally incapable of any useful work, nasty and annoying work will be created for them to do -- IIRC the example given was counting the hairs on caterpillars by touch -- and so long as they complete their service they can still be a citizen.
Helldivers though, is a satire of American post-911 jingoism. It's loosely inspired off of the movie, which itself is only loosely inspired off of the book.
As a result, trying to draw a direct connection from the book to the game is going to lead to a disappointing lack of similarities. I'd say the satire of Helldivers 2 is better than the movies, simply because the thing it's satirizing actually existed in the world in some meaningful way.
Correct in all regards. Verhoeven was a hack with an agenda who satirized a book that did not exist and openly admitted that he assumed
Starship Troopers was pro-fascist propaganda and that he had never read it. It's pure coincidence that he managed to make a pretty funny B-movie. As you say, Helldivers and the sequel are a much funnier take on the topic both because they're produced with more attention to detail and because they're not intrinsically slandering a genuinely interesting book and author by existing.