People always say before start a business your product has to solve a problem that people have. It seems to me that video games are for entertainment purposes and doesn't this seem a little too broad? In addition, one of the answers to this question, is that you have to find an audience and then build a product. But isn't that a little backwards for video games? Isn't the product created first and then the audience is built?
To make money you still want to find an audience when it comes to game dev ahead of development. You need this to understand the market, and what is likely to go over well, and what isn't.
For instance most gamers now adays tend to not deal well with difficult games, or only do so when the difficulty is offset by super accessibility. (like infinite lives and instant restarts.) Thus making a difficult game type that was the norm in the 90's or 80's likely wouldn't be received well by today's gaming audience.
Honestly though many of the normal startup approaches like minimal viable product and such don't translate well to game development. Though there is certainly much wisdom in getting prototypes and early builds done to test out mechanics and ideas in play testing early vs wasting tons of resources to find out down the road that your game isn't fun.
Well, the broader "problem" is "attention" what is going to engage peoples attention and make them part with money?
In most of life the key driver for parting with money is to remove some "pain" out of your life.
Games absorb peoples attention, provide mental stimulation (remove boredom) and take people away from their current throught processes.
In this respect they solve the same thing a good book does ... provide escape.
For me, video games fall in the fourth level of the Maslow pyramid : self-esteem.
But some people think that video games fullfill the whole pyramid, see for instance http://www.werkkrew.com/2008/07/09/maslows-needs-and-gaming/.