Quartz can form through a couple of ways. It can form from magma as it cools or crystals will form from silicon dioxide dissolved in water as the temperature or pressure drops.

The scans of rocks on Mars show the pattern of hydrothermal forms of quartz. This might happen when a meteor hits causing an increase in temperature and pressure near the edges of the impact crater. This might dissolve silicon dioxide in any water present then, when it cools, quartz crystals form.

I don’t know what they mean by “water circulation” but it does point to water being present.