Is the single engine Piper Malibu required to have a black box?
The short answer is that it probably does not require a "black box".
What you refer to as a "black box" is actually 2 things (and Orange!) a Flight Data Recorder and a Cockpit Voice Recorder. The rules on when they are required is broadly similar, however the data required to be captured by the FDR varies.
For the CVR:
Fixed-wing aeroplanes with a maximum take-off mass of more than 5 700 kg and for which the certificate of airworthiness is first issued after 1 January 2003 shall be equipped with a CVR with a recording duration of two hours
For the FDR:
[...] depending on the maximum certificated take-off mass and the date of first issue of the individual certificate of airworthiness. For example, provision 6.3.6 of Annex 6, Vol. I states that, all aeroplanes of a maximum certificated take-off mass of over 5,700 kg for which the individual certificate of airworthiness is first issued after 1 January 2005 shall be equipped with a Type IA FDR
The Piper PA-46 (aka Piper Malibu) has a MTOW ranging from 4,340lb(1,969kg) to 6,000lb(2,721kg).
Speculation about the recent incident, and the specific model intentionally left out!