As described, the marriage is not "built on lies". The marriage includes some lies. There's a difference. While it isn't a great thing that he feels he has to hide a harmless leisure activity from his wife, it can be okay for partners to have some privacy.
Privacy and hiding/lying/dishonesty are very different things. For me, the latter would utterly destroy my trust in the person who was supposed to be my best friend and life partner. I personally could not live that way. It is not my business to tell other people how to live, though.
Remember that radical honesty doesn't work either. Humans typically require some management of information in order to get along well.
Actually, it works incredibly well for us. Good communication skills are a pretty excellent relationship foundation, and bad communication skills (or refusing to communicate) is fairly likely to run you into trouble sooner rather than later. Feeling like you can't communicate or that you can't be honest with your partner is something I would personally see as a pretty serious red flag for the relationship. Again, I couldn't live with it. If my life partner is not my best friend whom I can be totally myself around and totally honest with, there's something majorly wrong.
Mainstream society puts a lot of social barriers between the genders and encourages what I think are seriously dysfunctional relationship memes. In my experience, doing a hard dump of all that nonsense from your brain and starting as best friends, gender roles irrelevant, has been an excellent foundation for a very low stress, drama-free, comfortable and happy long term relationship.
Possibly the fact that I have non neurotypical wiring is a factor. I function on a pretty transparent WYSIWIG interface, and I don't actually understand the point of social lies, hidden agendas and "harmless" deception, especially in the context of a personal relationship. I'm not sure I could effectively manage to do these things even if I wanted to learn how. And I really, really don't - all the mainstream social baggage looks horribly dysfunctional to me, especially when it comes to how male-female relationships are "supposed" to be. Yikes, do not want.
I'm very happy to have a best friend and life partner who is as weird and geeky as me, and neither of us ever has to lie or pretend or be anything except who we are. It makes for a very comfortable, low stress home life with lots of happy geekery. I don't think I could personally live any other way, but of course your mileage may vary. Not everybody is wired to want the same things in life, and that's pretty much what makes the world go round.