Yeah it can be a problem fitting it in, but if it's really what you want to do then you somehow have to manage it.
Engineering comes in lots of forms, "frontend" working with the clients, 3d models, etc. "backend" handling events and networking. And much more in between, if that's what interests you.
With a background in maths and data science, and knowledge of engineering? There are a lot of areas in Game Development where you could fit in. One that I might suggest is in "Game Design"? By this I mean a person who "thinks up" features (and/or whole games), does the math to calculate values of x and y, and the like. To figure out ways it could be exploited, and to circumvent them.
Using your data science knowledge to find out what parts of the game are used and where it could use further development.
Typically at our company we get given a game design document from the game designer, this can contain anything from a basic overview of how things function, to projections, maximum possible outcomes (think for example, the maximum amount of gold a player could gain from this scenario) etc.