Why is there a 5V linear regulator on this USB ATTiny85 dev board?
Your theoretical understanding of a voltage regulator's dropout voltage and operation is correct. It indeed requires at least +7V to operate within its specifications because its output voltage is +5V and its dropout voltage is 2V.
However, the voltage regulator is not where you think it is. It supplies +5V to the attiny's supply pins, taking its input from the Vin pin, and is used as an alternative when +5V power is not available via either a USB port or other power supply.
This, and your concerns related to dropout voltage, are confirmed by the part's specifications listing:

Tensiune de intrare (recomandat): 7-35 V

or translated:

Input voltage (recommended): 7-35 V

This presumably refers to the Vin pin, whilst the +5 V pin and USB VBUS alike are intended to be used strictly within the USB/attiny supply voltage specifications.