Measuring quiescent current of a voltage regulator
To measure the quiescent current of your regulator, you would need to measure the input current and the output current (as the input current will be the sum of load current and quiescent current for a linear regulator).

If you take a close look at the regulator datasheet



You will note that the minimum load current is specified for the adjustable version only; the true quiescent current is the adjust pin current for this device:



This is listed for the adjustable version only (so the designer knows how much current will need to be drawn from the regulator in the case the load may not take the listed minimum).

The conclusion here is that the fixed version (which is what is on your board, AMS1117-3.3) has been provided with a minimum load internally. That load is very likely the current in the voltage set resistors and probably some other physical load provided internally to the devie package.

The adjustable versions list the quiescent current as the minimum load current, but for guaranteed regulation, there may need to be another 5mA of load.

The datasheet shows the typical quiescent current at 5mA, but note 5 states:

Note 5: Minimum load current is defined as the minimum output current required to maintain regulation. When 1.5V \$\le\$ (VIN - VOUT) \$\le\$ 12V the device is guaranteed to regulate if the output current is greater than 10mA even though this note only applies to the adjustable version (the devices will all be identical except for the adjustment resistors and loading).