The carabiner was not used to anchor the kite. It was used to hang line laundry on the line.
And you're right, it doesn't sound like a lot of laundry to be hanging off a bit of metal...
But, in your example of how it was attached to the line, you inadvertently set it up in possibly it's weakest orientation, you've allowed lateral twist forces to be induced through your load weighting, not alot, but enough for a gate form like this to fail. Prussic loops will help a lot here, and when used properly will help the gate to load up properly, you might even get away with using your existing gates.But TBH do look at upgrading them, they are, in their base form, pretty poorly designed for any work much beyond convenient key carrying.
I'm no expert mind you, but I've done a bit of traditional rock climbing in the past and their sort of 'safety meeting' pack drill stays with you