Could a waterfall lashing onto a road lead to a landslide?
Potentially, a landslide could occur. Whether it would be a minor slip or a major fall depends on the geological conditions at the site, the force of the water and the duration that the site is impacted by the water.

In the video in question, the rock face above the road appears competent, but there are not guarantees. The main issue would be is the water undermining the road which could cause a slip and the road to slide.

The more loose the geological material is, the easier it is to dislodge it. Once one item moves a chain of events can occur where additional items are dislodged and a slide occurs.

In addition to high pressure water dislodging material, water acts as a lubricant, making it easier for rocks and regolith to be dislodged.

To minimise the potential for a slide to occur in such a situation, the surface of the road would need to be sealed very well and a very good drainage system installed that would move the water away from the road and the slope below the road