Is cutting one’s hair to look good or to impress someone else considered shirk (polytheism), especially if shaving the head is an act of humility to other than Allah, as Ibn al-Qayyim mentioned?

Shaving the head to gain admiration or to appear good is not shirk (associating partners with Allah). It is a normal worldly matter in which showing off (riya') does not fall under shirk. What Ibn al-Qayyim spoke about was shaving with the intention of worship and drawing closer to shaykhs, and this differs significantly from shaving for worldly purposes.