That resistor isn't going to offer much ESD protection. If you applied e.g. 1kV ESD, it would still permit 3.7A to flow, and that's assuming it's ideal. Remember, it's the discharge current that matters. It could permit even more, if for example the ESD arcs across it as ESD is prone to doing.
It does, however, protect the opamp against a large (but not ESD-large) voltage being applied to the input. Imagine applying 10V directly to the inputs in the lowest range (10k sense resistor), a fairly easy mistake to make. It could even happen just due to the DUT attempting to draw too much current and "saturating" the current shunt, which happens at a very low current with such a large sense resistor. You'd have 10V applied to the opamp input, 8.5V above V+, without that resistor. With the resistor, the current through the opamp's diodes will be limited to around 29mA - still not great, but definitely better than a direct connection.