I started professionally in the video games industry at 25, and as a producer at 26. Before that I was in retail.
That being said, video game development has been a hobby of mine ever since back when I was a kid (at 9 I wrote my first game program, and around 7 my first 'GDD' if you can even call it that).
I've seen more correlation between being a good industry developer and the age at which this started being a hobby than when it started being a job to be honest.
For example, people come fresh out of school can either be great or bad, and if you dig deeper, you often realize there always was (or not) an underlying interest of some kind and it makes the difference).
To a lesser degree, I've seen a few success stories of people coming late to the industry, but those with a passion managed to come in. It's a tough challenge because there's a lot to learn, and it's a bit harder to learn in our 30s (I feel old) but it's not impossible.
Then again, I've seen a lot of people 'try' to move to games without passion and saw them shredded by the industry in but a few weeks/months in many occurrences.
The most unsuccessful transitions I've seen were due in part to bad judgment on the HR part where they assumed that a 'good manager' in one field can manage 'any field' and I can certainly attest to the contrary in Video Games. On more than one occasion I've seen IT project managers feeling estranged beyond means in the video game world.
Now, granted, you've been offered a much smoother (and more sane) entry position which may result in a more desirably outcome, but I think the underlying question prevails: is your passion for game sufficient to turn it into a job, or in other words, do you feel you understand and like games enough that spending entire days deciphering their issues won't turn you away from playing games on your own time when the day's over?