Kids will ALWAYS watch a video or play a video game if there is an option to do so. You can't let it be an option outside of reasonable designated windows of time. Make sure there are interesting books laying around in all his "lounge" areas. Don't "force it" but make it easy.
My kids don't have video games, but TV is the same exact sort of evil, so we designate times they are allowed to watch (or play their friends video games). They get to watch TV for an hour at night while I make dinner and catch up from busy day. Then it goes off. The rest of their day they can read if they want, there are always stacks of good books around. Sometimes I force them (certain amount per day for school or before library books are due to go back whatever), or sometimes I let them play or go outside if they really don't feel like reading. In their rooms there are ONLY books, no electronics. Nice reading lamps, good selection of enjoyable books. They can read first or go straight to sleep at night. In the car, they have books. They can read, or look out the window and talk. We have never ONCE had a problem with boredom in the car, and we have been on many extremely long road trips.
The challenge is that every single one of their friends have video games, and they bring them wherever they go. So at any and all events, they want to sidle up to a kid with a game. Sometimes I let them, sometimes I don't. Sometimes I end up having to engage them in drawing a picture, or playing hang-man or tic tac toe to keep them occupied when I really wanted to zone out or read my own book, but that's the price I need to pay if I don't want them on a video game or watching someone else play a video game the whole time. They're young so I need to teach them how to entertain themselves with other things. If I did have video games around and accessible in the house, car, my tote bag, etc, my kids would never want to read or draw.
They know they can play video games when they get older, get jobs, earn them, buy them, and then fit them into their schedules after responsibilities are done. By then they will be great readers with the habit ingrained.
So many parents tell me, "My kids just prefers games and videos, they don't want to read."
You have to set up your home life to support the habits you want to build. If you only want your child playing games rarely after reading, schoolwork, practicing instruments and playing outdoors, then those are the rules you have to set. The games are put away until they are "allowed".
It's awesome that your son is a good reader. He will grow to like the habit. It helps if they frequently see you reading. My kids know I look forward to windows of time where I can read, and they see me doing it, so now they are doing it too. I've always given them re-caps about what I'm reading about, and they'll ask me what's happening in my book...It takes enforcing at first and that's OK.