This is a fairly nice layman's description of 'ACARS pings' that have been wildly misunderstood on this thread...
Understanding ?satellite pings? ? Tim Farrar - The Malaysian Insider
For those still reading - this gives an overview of ACARS:
https://www.sita.aero/file/1569/Aircom_new_generation_services.pdf
There are some AEEC standards documents in that document that contain the protocol definitions of ACARS.
From the document: "the AeeC Characteristic 741 for the satellite Data Unit specifies the use of an X.25 based protocol, which Inmarsat originally intended to be used for packet data communications across the AMss network. this complies with the protocol specified in the ICAO AMss standard described later in this document."
So it uses X.25 - there's some DTE address fields there.
It seems the ACARS "SATCOM" data stream in this aircraft was based on the Inmarsat Swift64 service and these terminals use an ISN which is a "12 character Inmarsat Serial Number" - so there's the layer 1 ID.
Although I haven't found those standard definition documents for this service, it seems like these 'pings' would be addressed directly to a terminal address (i.e. unicast to the specific ISN) rather than some random broadcast/multicast across the whole beam/coverage area (pointless thing to do).
X.25 can do the same thing - and the AeeC can do the same on top of that - apparently (according to AEEC 620 standard for ACARS) it uses a 7 letter IATA address (from the aircraft registration mark).
So there are three different addresses at three different layers that would be able to identify the signalling terminal.
As an aside, especially when talking about mobile/cellular phone systems, just because you know something about one system does not mean every system works similarly - (this thread contains mounds of rubbish on this topic).
Remember that there are 2G, 2.5G, 2.75G, 3G, 4G, LTE systems using Analogue, TDMA, CDMA, W-CDMA, FDD, TDD, etc all on different bands, with different design trade-offs and varied methods of implementation and completely different performance characteristics (and I haven't even mentioned the Chinese varieties like TD-SCDMA).
BTW - in the beginning "ping" was a UN*X utility designed to send ICMP packets for IP networks - named after the Sonar 'ping'.