I recently quit my job in game development where I was there more than two years, in Illinois. My contract had a clause stating that I could not work in game development within something like a 50-mile radius (basically, the entire urban area in this region) for a period of one year. I have a new job not in game development, but want to do game development on the side.

Is a non-compete in this case enforceable - that is, is preventing me from doing game development a "legitimate business interest" in the eyes of Illinois courts?

As always, discuss with a lawyer.

There is always the spirit of the agreement and the letter of the agreement. There is the nature of the industry and your right to earn a living. And there is the probability that an employer will go through the cost of enforcing it.

In practice, non-compete agreements are not enforced unless there was some serious harm to the former employer.

If you were jumping from a high-profile job at one company to a high-profile job at another company you would likely have many fans that would switch. That could do serious harm, and that could be enough for an employer to attempt to enforce the non-compete.

If you were working on a big-name product and immediately started a direct competitor for that product, that could do serious harm, an employer would likely attempt to enforce the non-compete.

If you were building your hobby project that was very similar to the product in your day job, and you release it around the same time as your day job's product and end up drawing customers away, an employer would likely attempt to enforce the non-compete.

But if you are just a peon in the company and you are not really competing with the company and your transition doesn't cause any kind of conflict or harm to the company, they probably won't care. And if they did care, they probably would not invest the small fortune needed to enforce the agreement.

To add another "I'm not a lawyer" comment. Unless you are poaching current employees from your old job or taking the knowledge you learned to create a product to compete with them it probably isn't worth the cost to try and take you to court.

You need to review the terms of the contract with the no-compete clause.

Typically they specify a Competition vector, meaning if your hobby of developing is not in competition with them there is no violation.

If there isn't such a condition, the clause likely cannot be enforced in the first place, as the legal position of no-compete clauses is that an employee could learn a technique which is not patented or otherwise protected and then use that technique to elevate potential competition against them in the same market.

If the contract includes terms regarding Competition, and you are not competing in some way, you are in the clear.
If it does not, while the legal standing is highly suspect, you should avoid violating it regardless.
Take a ride with a mobile to outside the specified area, find a nice park and work there....
or speak with an attorney.

Or do something no one seems to think of - speak with the company you entered the contract with and request written exemption for the purpose you intend.