Shrikhand starts by hanging yogurt in cloth for hours. Everything the dessert is comes from that step, since nothing else in the recipe thickens or concentrates anything.
Draining concentrates everything but water
Yogurt is mostly water held in a protein network, with whey the fraction that drains away carrying dissolved lactose, minerals and some protein.
Removing it leaves the fat and the majority of the casein behind in a much smaller volume. The result is denser in solids without a single ingredient having been added.
Because flavor compounds concentrate along with the solids, drained yogurt also tastes noticeably more intensely of yogurt than the original did.
Texture comes from the protein packing together
As water leaves, the protein particles are forced closer together and the network becomes tighter. That is what produces the smooth, spoon-holding body the dessert requires.
Whipping afterward breaks the tightened network into fine fragments, giving the silky rather than granular texture that distinguishes a good shrikhand from a merely thick one.
How long the yogurt hangs decides where on that scale it lands. A short drain gives a soft pourable dessert, while an extended one produces something dense enough to hold a shape.
Sugar reverses part of the work
Sugar is hygroscopic and pulls water out of the protein network, but it also dissolves into whatever water remains and loosens the whole mixture.
A shrikhand thins after sugar is beaten in and then firms up again on chilling, which is why the consistency is judged after refrigeration rather than at mixing.
Powdered sugar is often preferred because it dissolves without needing extra liquid, and any undissolved crystal is detectable in a dessert this smooth.
The starting yogurt determines the yield
Full-fat yogurt drains to a richer result, since fat does not leave with the whey and its proportion in the remaining solids rises.
Low-fat yogurt gives a drier, more chalky result at the same drainage, because the concentrated protein is not being softened by fat between the particles.
Making it with US supermarket yogurt
Greek yogurt has already been drained, which shortens the process considerably, though brands vary in how far they have taken it and some are thickened rather than strained.
Plain whole-milk yogurt drained at home gives more control and a cleaner flavor. Since the process involves dairy sitting outside refrigeration, doing the draining in the refrigerator and following standard dairy handling guidance is the sensible approach.