So, I'm pretty sure Octodad: Dadliest catch is set in Lovecraft's fictional universe, and not just because of the stained-glass Cthulhu in the church.
Firstly, there is the daughter. In the aquarium, she mentions having dreams of one day living under the sea. Sounds a lot like those Innsmouth folk, doesn't it? This would suggest to me that Stacy and Tommy are actually Octodad's biological children, and Octodad is associated with Dagon's fish-men.
Then there's the chef, who's a lot less subtle. He talks about a war, and the deadliness of cod, and cutting men open to find only "piles of fish." And, at the end, is surprised to receive Octodad's forgiveness in spite of this war. The US government bombed innsmouth and torpedoed the reef at the end of Shadows over Innsmouth - perhaps Dagon's armies retaliated against America (or all of humanity) and were fought off. So I wonder if Octodad is perhaps a veteran of that conflict.
Thoughts? Comments? Observations? I'm curious to see if there were any subtler hints that I missed.