I did game development in a previous lifetime. Probably half my day was implementing algorithms and thinking about the correct data structure for a problem.
I spend less time these days implementing algorithms. However, you need a good understanding of algorithms to decide between using ActiveRecord or a service layer. You need a good understanding of algorithms to pick between a relational DB, a key-value store, or a document store.
Maybe you aren't picking difficult enough problems if you don't have to think about this kind of stuff.
I've mainly done web development and typical university style assignments for the bulk of my programming experience- barely encountering algorithmic problems that weren't well defined.
Recently, I started creating a throwaway physics/game engine for fun and it is an awesome way to learn some really cool algorithms. Also, I did a small image manipulation app that exposed me to some cool stuff as well.
As a new grad it definitely pushed me more towards game development- would you mind sharing your reasons for leaving?
Game development is hard. The average engineering role at a games company involves a lot of work on hard deadlines.
It's also tough for some engineers because there's usually a very clear product vs engineering divide -- you're implementing stuff other people come up with, and when they change their minds you throw it out and do it again a different way.
That said, making games is also a ton of fun and is a great way to be exposed to a lot of interesting engineering challenges. If you like games and you can put up with the issues above, you should definitely consider it.