“The article said it was a Tandem kayak. That would mean there were holes for the two adults, and they somehow stuffed the kids in with them.”
The article says it was on open-to kayak. That means there were no holes.
Here's an example of a 13 foot open kayak. Essentially, a canoe. OK for going down a calm river in summer. Only an idiot would take one out into deep water far from shore.
You are more right than I am.
It said “tandem open-top kayak”, whatever that is. It sounds like a small pointy canoe with very little freeboard.
An open top would make it very vulnerable to taking on water and swamping. Five people would make it too crowded to bail.
My wife and I once took two toddlers in a 14 canoe on a small pond, no waves, glass smooth water, and I thought the canoe was overloaded. With rough water, there is no way that would have worked.