Yes, but those don't work for heavy applications like this. They usually have a weight rating, one well under a full rack of clothes... Just put it into the wall studs, it's easy enough.
Well please excuse my German stubbornness... The drywall anchors (thanks @[email protected] for the word) I know and often installed were certified up to 40 kilogram - per anchor (single layer drywall, one anchor per meter as a rule of thumb). A rack full of stuff like in the picture won't have more than 50 kilogram load (static load - please tell your kids not to climb onto the shelves) so two such anchors would have handled that easily, and there's plenty of room to install more than two.
I understand that other parts of the world live up to other standards.
Agree - have previously fixed a wooden bed frame to drywall using 4 such anchors with no problems. Not as daft as it sounds - it was probably only supporting 20% of the bed and the weight on it, so unlikely to reach 100kg even with 2 people in/on the bed!