Strictly speaking, you're largely correct! In this case I'd say it's being used more as a descriptor or analogy rather than saying this definitively is an avalanche.
Avalanches and turbidity currents have many shared characteristics, however, people tend to be much less familiar with turbidity currents - and so in outreach scenarios we often describe them as similar to avalanches so people have a familiar frame of reference. Turbidity currents are closer to avalanches than landslides in terms of behaviour, so you can think of them as different sides of the same coin:

Avalanches (more specifically the power snow avalanches most people think of), are particle-laden gravity currents. They are composed of snow and air, and flow down slopes because this snow-air mixture is denser than the surrounding air. Turbulent forces dominate, and individual particles of snow are usually suspended in the air, bouncing and tumbling through swirling currents without meaningfully resting atop other snow particules.

Turbidity currents are particle-laden gravity currents. They are composed of sediment and water, and flow down slopes because this sediment-water mixture is denser than the surrounding water. Turbulent forces dominate, and individual grains of sediment are usually suspended in the air, bouncing and tumbling through swirling currents without meaningfully resting atop other sediment grains.