I think a game should be enriched by outside lore, but in no way require it. The biggest name I can think that does this right is Starcraft. I love the story/lore of Starcraft, but I have only ever played the games. Recently playing though the Legacy of the Void, I looked into some lore things and found a wealth of knowledge that came from the massive number of books and other media related to the series. What Starcraft does right, however, is that the games never seem lacking. The story within the games are entirely self contained, but some of the off hand comments are references to events that have never been covered in a game. For example, not knowing who "Adun" is doesn't hurt your enjoyment of Starcraft because the name is only used as a greeting/battle cry. My own curiosity led me to looking into who Adun was and then let me find out that there is a massive backstory behind who Adun was, etc.
I think games that try and do world building need to have in-game information about any relevant lore. Mass Effect did a great job with the codex because it categorized the information properly. It is a little excessive to have explanations for so much, but by labeling things, you at least knew that you weren't missing out on major plot points by not reading the entries about how medigel worked. Having those excessive entries is nice, but it needs to be properly labeled so people don't feel compelled to read all of it if they do not want to.
Conversely, I really feel that Bethesda does a pretty poor job with this. I personally never liked the Elder Scrolls series as a story and I feel that a part of that is because there is no easy way to find out the basics of what the lore is. The games add to the lore but there is no way to easily learn about previous events within the games. Fallout as a series I am more interested in and actually did bother to read through a lot of the previous lore, but again this required me to find it out through wiki-walks and google searches. The backstory is incredibly interesting but there is no real way to learn about it within the games themselves (haven't played Fallout 4 yet so I'm assuming that it hasn't resolved this concern). I guess I can kind of understand the problem for Fallout because Bethesda didn't create the original lore, but it seems incredibly short-sighted for The Elder Scrolls games.
The only game-related book I have ever read is the Metro 2033 book. And again, I didn't feel compelled by the game to read it. I had just finished Metro 2033, Last Light wasn't even announced at the time, and I just wanted to experience more of the story. Since the game was adapted from the book and I was wanting to experience the world, the book was a perfect option.