Halliday & Matthiessen (2014: 225, 225n):
Processes of all types unfold through time; but the way the process unfolds may vary from one process type to another. In particular, processes of the ‘material’ type tend to differ from all other types (with the partial exception of ‘behavioural’ processes …), and this is seen in how present time is reported. The unmarked tense selection is the present–in–present (e.g. is doing) rather than the simple present (e.g. does) …
The present–in–present serves to narrow down the present from the extended now of habits and ‘general truths’ that is characteristic of the simple present with ‘material’ clauses …
The narrowing–down effect of the present–in–present is not brought out by the names most commonly used for this tense — the ‘present progressive’, or the ‘present continuous’.