Hello,
The player automatically sends an API call to update the play count [and other analytics] when the user plays a video.
The API is called stats->collect() and you can see the call being made when running a HTTP sniffer.
Note that plays are only counted when embedding a player outside of KMC and also that the stats are updated once a day in a batch operation and not in real time.
If you want to implement your own alternative analytics mechanism then yes, you can write your own player plugin to do so.