When the compressor shuts down the pressure will be lost at the outlet of the compressor and the downstream gas will flow back.
A standard check valve will allow a considerable volume to pass back (as the valve will take a while to close). A non-slam valve will close rapidly and hold the downstream pressure. [The 'non-slam' isn't specified for its ability to stop slamming - it is just its quick closure].
The nozzle non-slam valves are better as they are 'true' non-slam. Dual Plate style may be advertised as non-slam but realistically the performance is far inferior - it benefits from a spring but most of the closure force comes from the gas back-pressure.
I personally would not specify a separate 'non-slam' valve on the discharge of a reciprocating compressor. As has been mentioned - the compressor will have an integral valve which will be sufficient.
Non-Slam check valves are so-called 'high integrity' check valves so they also find applications on well-heads; they can be used at the end of lines before mixing (no need for non-slam). In compressor applications they are also used on the suction side of multi-stage units... in the event of plant trip the inter-stage pressures will be maintained.
Just as a footnote - It is critical that the discharge check valve is installed immediately after the anti-surge take off. Quite often the valve is installed downstream of the heat exchanger which can make the valve less effective (the valve will only 'check' the volume downstream').
I hope this makes sense (i'm writing very late at night
)