Compassion and Motivation
I haven't studied clinical psychology.

When I read this comment I discovered it has a doctrine or theory about something it calls "behavioral activation" --


  In the case of depression there is ample clinical evidence for behavioral activation as a mean to counter a clinical depressions cognitions, emotions and behavior.


Using Google I found a quick description of "behavioural activation" here: Behavioural Activation: Behavioural Therapy For Depression Treatment

That theory sounds plausible (e.g. worth testing).

Anyway I think that adds insight or background information to the quote in the OP ...


  When your goal is to help another person [out of compassion], then your reward system will be activated when you’re meeting that goal


... i.e. at least enough to help understand what Dr. Weng was saying.

And if that ties in (as it seems to here) to being a therapy for depression, that might answer your question about motivation -- because I think that depression is antagonistic to motivation in general.



Secondly, this article ...

Why You Procrastinate (It Has Nothing to Do With Self-Control)
If procrastination isn’t about laziness, then what is it about?

... claims that procrastination is a problem of emotional regulation -- i.e. it's caused by wanting to avoid emotional problems which you associate with the task that you're procrastinating about (and preferring tasks which give a short-term reward).

So perhaps this (quoting from the article cited in the OP), "the compassion training also seemed to strengthen the brain’s ability to regulate emotions", suggests another way in which it might improve "drive" -- i.e. by reducing a "need for procrastination".

I guess a question (perhaps your question, which I'm not sure this answers) is whether it improves all emotional regulation, or only the regulation of emotions associated with the suffering of others (compassion).



Thirdly, this article from a while ago, The Pursuit of Happiness suggests that with meditation (it didn't say what kind -- the sort practised by "the Dalai Lama's lamas, the monks") lets you "train" the mind to be "happier" and remain happy under adverse conditions (including specifically unpleasant external stimuli).

That too fits with the theory of what causes procrastination.