So my analysis is biased
For the ship scenario the ship needs to completely cook the missile, the missile is protected by ceramics and seeing with AESA
For the J-36 scenario the missile has a glass dome and is using a heat seeker. .2 seconds of direct laser is enough to blind it and destroy detector elements.
Larger airborne lasers have been tried and failed, i.e YAL1 needed magnitude more power, but that was to intercept ICBMs shielded to survive rentry.
100 kW and 10s dwelling in atmosphere theoretically works for AA intercepts.
What's slept on is it lasers also potentially like scifi tier infinite ammo laser gun vs subsonic targets... like drones and cruise missiles. You don't have to line up gun runs (which J36 doesn't even have). The limit is basically how fast heat exchange dumps laser heat into fuel burn, but lazy llm math suggest like... multiple targets per minute with off boresight engagement - i.e. all targets within 10km cone/swath. This absolute game changer / flips economics against any budget drone precision complex adversaries.