Are the highlighted groups of notes in the example below to be played together? My theory is that these groups of notes were drawn at a distance from each other in order not to clutter and create confusion.
Your theory is correct: these notes are written offset from one another to be legible. They are to be played simultaneously.
Since hemidemisemiquavers are written as such, then the dots on a single stem should be played simultaneously. Otherwise it'll be a fast arpeggio, which is sort of what the hemidemisemis are.
Also why put an arpeggio sign when that's about the only way to play hemidemisemis.