Thanks for the explanation.
I just tried the --renderer sdl command, but the unexpected result was this:
it started on the laptop screen only.
At the second attempt, both screen were on (mirrored).
After closing SuperTux, I had to use the xrandr specific command to get my
external screen back.
The good news is that even at the biggest available resolution (3200
something, way bigger than my external screen resolution), it's super fluid.
The result on screen is exactly the same as the smallest resolution (640
something).