Thank-you Randy.
This is interesting: once I booted the Rpi for the first time (and chromium did appear), the Rpi prompted me that a number of updates were available (by means of the "update icon" that pop-up on the taskbar.
I selected to install them, and I guess from that moment on, chromium is not automatically starting anymore.
So there must be something, in those updates, that breaks picochess/chromium.
It could be the graphics environment, maybe a change between LXDE/X11 (which I think is what we have at first boot) and Wayland/Wayfire which probably gets installed and used by default after the update.
I'm saying so, since after the update, I noticed a very small change in the taskbar appearance, which I initially did not notice.
I'm reflecting on the best approach here:
Do I have to revert back to the previous LXDE/X11, or shall I simply fix the autostart, to make sure that it gest executed also under the new environment? If the Rpi from now on, makes use of "newer" components, like Wayland/Wayfire, maybe the right approach is to adapt the auto-start.
Have you encountered such situation, and if yes, what was your approach?
Andrea