Just to chime back in
The KoC tends to do a lot of fundraiser type events for the parish, they are known for the fish fry on Friday's during Lent - which is generally their largest event and fundraiser during the year. The funds that are raised go to various parish activities and groups, generally not just to the KoC. At my parish the fish fry one year paid for a new parish playground for the kids. So, while their events tend to be "secular", they really contribute a LOT to the life of the parish and the events become something that the whole parish can enjoy and rally around as a way to know one another more than just going to Mass once a week.
I am sure the "spiritual" aspect varies by parish, but if one is a member and one wishes to add more spiritual activities for the men I am certain that the local KoC would be more than happy to add that to their schedule. As with pretty much any church group, what you get out of it and the activities they do are largely driven by the people in the group and the member themselves personally. It is sad that the previously mentioned leader felt the KoC was too secular or social oriented, I think he was missing the most valuable aspect to the larger parish life. If he was the leader he needed to add some more spiritual activities, work with the parish priest on how to do that.
The meetings tend to be more of a Men's club to hang out and socially interact, which honestly most men sorely lack. Having the KoC is a good way for Catholic men to gather together and socially have a nice time, there are not a lot of other places that enable that. Generally a meeting will have "free" (you member dues or donations pay for it) soda, beer, and wine as well as snacks.
However, the social interaction along with prayer and enabling the parish to have a more fulfilled lifecycle is very valuable.