How can a small ducted fan produce a large amount of thrust?
Thrust depends greatly on diameter, so your curiosity is reasonable.
Why:  A first-principles answer says that (static) thrust depends directly on the rate of mass flow through the duct.  Because the duct's area is small, the speed of air through the duct must be large, and thus what must also be large is the fan's (static) pitch speed and its RPM.
See https://www.grc.nasa.gov/www/k-12/airplane/thrsteq.html for the case $p_e = p_0$.
For 175 N thrust, Schuebeler says the fan turns at 20,000 rpm and needs 12 kW.  Those numbers are not vastly different from an unshrouded 15 cm propeller, or a small turbine (a JetCat P220 does 220 N at 725 mL/min, converted via kerosene's MJ/L to roughly 450 kW; there's much more waste heat in a turbine's exhaust than in a ducted fan's gradually warming battery pack).
How:  Tight manufacturing tolerances, so the blades don't vibrate from imbalance, so the blades don't deform or break at high rpm, and so not too much air leaks around the gap between the blade tips and the walls of the duct.  (The same applies to turbines.)