So maybe I'm just completely dense, but I can't seem to find the answer to this through any online searches.

I just got Innsmouth Horror, and on the board, there are three spots (one off Devil Reef, one off Y'ha-nthlei, and one off Joe Sargent's Bus Service) that I can't find any information about. What are these scary-looking green gate-ish things? Are they just to denote portals that monsters move through if they're moving from one of the isolated locations?

Those are Vortex spaces. They are the primary driver for the Deep One Rising mechanic. If you obtain Dunwich Horro r sometime in the future, it will use a similar mechanic.

You can find the rules in your rulebook if you look again, but I can summarize the important points here:

1. Expansion boards never have a monster limit. Unlimited monsters can thus occupy an expansion board.

2. To counter this lack of a monster limit, Vortex spaces exist to eat up monsters.

3. Investigators can never enter vortex spaces. They are for monsters only .

4. If a monster enters a vortex space it is removed from the board. but it also triggers two effects: 1) the terror level increases by one; 2) the board mechanic activates. This is also true for the Dunwich Horror board (but the board mechanic is different). Kingsport has no vortex spaces; its mechanic is triggered in a different way. Kingsport still has no monster limit but with no gates opening there monsters are very rare and don't need to be regulated.

5. Innsmouth's board mechanic is that a token is added to the Deep One Rising track. Unlike the Dunwich board, there is another way to add tokens to this track: whenever a gate is prevented from opening by a seal or by Kate's ability.

So, that's how Vortexes work and that's partially how the DoR track fills. You're probably already aware how to counter the DoR and the penalty for failure. Note that the Martial Law mechanic is completely independent and unrelated from the DoR/Vortex mechanics.

Thank you. I saw that portion of the rulebook, and apparently I can't actually comprehend rules unless they come with pictures.