I used to work at DICE (EA), and other gaming companies with no degree. I never heard anyone required a degree. Some of our best coders were self taught and so were many of the artists.
Artist = Portfolio is king. If you make awesome art, no degree is required.
Level Designer = Portfolio is king or a pupular game mod, or maybe your own game (Maybe a C2 made one) to show your skill.
Developer/coder = No degree is required if you know what you're doing and are a complete nerd.
Even if a company doesn't use C2, completing a full good game with it, will show you have the knowhow about the fundamentals of the game design process, so it's always good.
It all depends on what position you're aiming to get. You wanna make game engines? Then u better learn some proper coding language. Games industry has tons and tons of positions, some doesn't even require any particular skill at all. My team leader at EA used to be a carpenter before he decided to work in gaming. But as a team manager, just project managing the development. Many companies also use their own in-house tools and editors, so you have to learn new anyway.
So all in all, depends what you wanna do, or rather how hard you are willing to work to get there.
A degree can help in the more technical positions but besides from that, not really required.
I'm also EA alumni I was pretty much going to respond with what you said. OP didn't state what role they were looking for, a degree helps you to understand the various roles in game development but is not 100% necessary for games jobs if you have some experience and a portfolio. If you were to become a game designer I think a portfolio of games made in C2 would suffice. If you were to become a games programmer then a game made in C2 wouldn't be enough experience as you don't really know a programming language, so you'd have to do a degree or take some online courses. I worked as a dev for a short while at Lionhead and this was from just learning Kismet and UScript within Unreal Engine 3 in my spare time, creating some demo levels and learning how to fix bugs with the scripting language.