I'm not sure that JSON has enough details to use.. I see SDS_P1 and SDS_P2 values (along with temperature, humidity), but I don't know if either SDS_P1 or SDS_P2 is a PM2.5 value that the script needs.
Looking more into it .. the SDS_P1 is the PM10 reading and SDS_P2 is the PM2.5 reading. The firmware JSON return only returns the instantaneous value at the time of the local query -- no trending/historical data such as returned by the PurpleAir JSON query, so I think the PurpleAir script is not directly adaptable to the Luftdaten due to lack of extra data needed by the script. Sorry...