Insulating gloves are not mandatory.
The instruction manual states "Turn off the power of this tester when making connection changes to cables and connection bars," so this is equipment that should "not be operated while live."
There is no problem with the lightning surge test itself, but after the lightning surge test, voltage may remain at terminals such as the input voltage terminals of the EUT, so when touching them, it is advisable to perform static elimination or voltage detection to confirm that no voltage remains, and take measures to prevent electric shock.