This is a pet peeve as a climber. The article lists "free climbing" as something that an insurer might refuse to cover. This is most likely incorrect, as the immediately preceding section suggests it would cost you an extra $1500 a year if you engage in rock climbing.

The bit that's incorrect here is that "free climbing" encompasses many forms of rock climbing. "Free" in the context of "free climbing" means that vertical progress is made solely by climbing the rock itself.

This is as compared to "aid climbing", wherein vertical progress may be made by affixing some form of gear to the rock, and climbing said gear, or something attached to it.

The article most likely means that if you free solo, you're uninsurable. Solo in this case meaning, without a partner to catch your falls.

E.T.A. Note also the existence of "aid soloing", and "rope soloing", both of which are done without a partner, but with varying degrees of gear in place to catch you should you fall.

Also note that absent the qualification of "soloing", rock climbing is generally understood among climbers to mean the kind that is done with a partner and a rope. Among climbers, bouldering is understood to include climbing routes of low height ("problems") without the protection of a rope, but generally with the protection of a crash pad (big foam thing to land on).