Can someone tell me how many hours a day does a video game composer typically works? Is it the same as a music producer?

There is no one correct answer to this. Anywhere from a few hrs - 24 hrs, depending on deadline, what needs to get done, etc.

Cheers.

A quote from the mighty Jesper Kyd:
"It's not unusual for me to work until 04:30 in the morning but I try to stop work around 02:00 am every night. So I start work in the studio around 10:00 am, work until 18:00. Take a break and usually get back to work around 22:00."

As Jeff says, it mostly depend on your deadline(s). However, Jesper Kyd schedule is quite extreme. If I were composing at the same pace, my ears would ring badly and it would prevent me from playing a single piano note for the next 5 days^^. So deadline + hearing endurance.

Yes, it's all about deadlines.
Most composers are working very long hours.
It's a passion and a lifestyle more than it is a job. So you work whatever hours it takes to get the job done, probably at least 12 hours a day, which can include working most of the night until early morning.

How can you manage not to have your ears bleeding with such a schedule? They need rest. Working 12 hours a day for several months is likely to trigger tinnitus or hearing loss and eventually shatter your ambition into pieces. Playing music is not like writing: it impacts your body in the long run.

Work at low volumes.
Of course it is tiring, but that's how the music business is.
You'll get tired, but you won't damage your ears if you work at normal volumes, especially not on headphones.
And projects last a few weeks and then there is often a gap before the next project. So you work 12+ days for a while, have a week off, then start again.

Not that I am complaining - but why was the threat title changed?

Too threatening

Learn to accept what your unconscious mind tells you - it does 80 percent of your thinking, no matter what, so you may as well learn to listen to it.

I do this by taking walks every day, it allows me to let whatever I'm working on gel in my brain. Sometimes this happens while taking a nap, just before you go under - the answer to whatever was bugging you becomes clear - neuroscientists call this the "aha" moment; for me, it's when the bridge of piece starts to come into focus, or how I might clean up a mix by deleting something I thought was precious.

Many of my best decisions have been made away from the studio - even while working on deadlines.