I thought an interquel was a game which took place between to other games and connected them together. It's not something which runs concurrently along side the original story as this page suggests. Half-life: Blue Shift is not an interquel because it doesn't link HL and HL2 together.

The wikipedia page about this has a good example where it says Metroid Prime is an interquel because it bridged the story between Metroid and Metroid 2 as it takes place between them.

I think the intended page was game which run parallel to each other, which would work for the games listed.

The description describes what it is meant to be -

A game that takes place during the events of another game.

You're making up vague confusing words for things that already have proper names. Side-story, gaiden, etc. Poorly conceived concept. If it takes place between game 2 and game 3, its a prequel. Its taking place before the last game. Star Wars episode 2 takes place between 1 and 4. Its a prequel to the original trilogy, sequel tpo the new trilogy. Not an interquel. If it takes place parallel, its a gaiden, its a side -story. Not an interquel. Peace Walker is a prequel (its events are relevant to the main hero,main villain, main story), Rising is a side story (events relevant only to fleshing out a side character, just like a Vamp origins game would be a side story, not a sequel) , Other M is a prequel, a game about the origins of some random bounty hunter in Prime would be a side story, etc.