Why is an earth continuity tester necessary to measure a resistance between a protective conductor terminal or a protective grounding pin and a protective grounding part on a chassis?

You can use other testers to only measure a resistance, however many safety standards specify a test current to flow through a DUT.
To meet such standard requirements, you need an earth continuity tester.

For example, IEC60065 (Audio, Video, and similar electronic apparatus – Safety requirements) specifies that the test current is 25 A and the allowable resistance value is 0.1 Ω or less.
In this test condition, if a DUT is broken down and its AC line will be internally connected to its chassis, high current will flow through the DUT.
The earth continuity test verifies whether the DUT can allow a path for current flow to the earth under fault conditions to prevent electric shock (ensure the safety) by flowing a test current (25 A or more) through the earth line inside a product to the connection line to its chassis.
In UL60950-1 (Information Technology Equipment – Safety- Part1: General requirements), the test current is specified as ‘twice the rating of the circuit under test’.
If the rating of a DUT is 16 A, the test current will be 32 A.

TOS6210 can apply a high current (max. 60 A) and perform a voltage drop value-based testing to meet the requirements of UL60950-1.