Earthquake Insurance usually will cover the cost of damages due to a landslide because the landslide just like an earthquake is a movement of the earth.
However you would have to check with your insurance company to be sure if your earthquake insurance will actually cover the cost of the landslide.
Some insurance companies will have the landslides covered under different terms of the insurance policy and may require you to purchase additional insurance coverage to be covered by the insurance company for the landslides.
For some insurance companies the insurance company covers the landslides under an insurance policy known as a “Difference in Conditions” policy (which typically offers all-in-one protection) for earthquakes, landslides, floods and even mud flows.'
Insurance companies and there policies can differ so it's best to ask the insurance company directly to be sure 100 percent.
However usually the landslides are covered under the earthquake policy.