Is the problem possibly that I missed changing the ATC frequency at one stage and things got out of sync? Especially after take-off there's a lot going on for one pilot and getting to the radio to change the frequency manually doesn't always happen in time.
There was a five-minute lapse between the time you were told to contact Departure and the time you did so, and that may well have thrown the altitude routine out of sync.
04/04/2018 21:44:24: 980 - Transcript: 'Saudia 773 Contact departure on 123.6 '
04/04/2018 21:49:39: 160 - Transcript: 'Departure Saudia 773 Out of 5 thousand for Flight Level 330 '
It looks like the comm frequency did not change to Departure until just before you made contact, so if the comm frequency changes will not work with this particular third-party aircraft you may need to do it manually.
(Still getting 'maintain heading 360' (or whatever) error BTW.. after which ATC goes quiet for the rest of the flight. I think this is due to be fixed in an upcoming update?).
I think this bug occurs in rare situations, after you have received clearance for an approach at pilot's discretion. See the following for a workaround until it gets fixed: