It's not quite the stable marriage problem, because in the stable marriage problem you're trying to find an optimal 1:1 pairing. It's also not the NRMP problem because in that case, residents are only matched with one hospital in a year. Here companies are matched with multiple investors, and investors are matched with multiple companies.
But regardless, I believe the algorithm is roughly the same as the NRMP algorithm: you run through multiple rounds where you look at each combination of company and investor. If both sides would prefer that they meet with each other, rather than the people they're already paired with, then you reassign them. Once you've done that several times you arrive at a stable state.
Yes you are on the money. There are also some additional constraints, e.g., we don't want to match startups with multiple investors from the same fund.
Well, with the constraint that no startup wants to have multiple visits with the same investor (and vice versa) - so you need to rerun the algorithm with the earlier matches removed from a preference list.