The engine monitoring system sends messages via ACARS to Rolls Royce as and when certain parameters change in the engines. If ACARS is unavailable then the aircraft attempts to forward the data via the INMARSAT system. Malaysian Airways chose not to pay the subscription fee for the satellite service, although the aircraft satellite transponder remained active.
So the aircraft satellite transponder just sends an hourly data ping to the satellite confirming the system is there, similar to a mobile phone on standby or emergency calls only setting notifying the network of its availability and location.
The pings that appeared out of schedule were in all likelyhood a response to some change in the engine parameters. Because ACARS was unavailable, an attempt was made to transmit the data via INMARSAT. A ping was sent to establish communication. The satellite recognised that no paid subscription was in force, so the request for further data transmission was rejected.
Everything worked exactly as it was supposed to.
The final partial ping can be attributed to power being interrupted to the satellite transponder and it powering up and running a self test program that was interrupted by losing power again. Just like turning a mobile phone on and off again before it has finished initialising. A data burst is sent to the network saying 'I am here'.
It would be reasonable to assume that the final partial ping corresponds to the approximate time the engines stopped due to fuel exhaustion and power was lost to the electrical systems. The satellite transponder is not considered an essential system, so it would not run from the RAT generator if deployed.
Everything points to the system operating entirely normally including the out of sequence pings.