Per narrator's comment above [1], a better way to explain the difference is that, for insurance, the insured doesn't want the event to happen, even knowing they'll get a payout, while in gambling, the insured wants the event to happen because of the payout.

This nicely aligns with what the practice of insurance actually involves: they do a lot to ensure that the client doesn't want the insured event to happen.

[1] https://news.ycombinator.com/item?id=23527972