why the interactive mode of my gnuplot installation won't rotate when it will for batch.dem files and also for Octave

Type in pause -1. That enabled rotation for me!

does adding set mouse make any difference?

(from the gnuplot doc)

The command `set mouse` enables mouse actions. Currently the pm, x11, ggi,
windows and wxt terminals are mouse enhanced. There are two mouse modes. The
2d-graph mode works for 2d graphs and for maps (i.e. splots with `set view`
having z-rotation 0, 90, 180, 270 or 360 degrees, including `set view map`)
and it allows tracing the position over graph, zooming, annotating graph etc.
For 3d graphs `splot`, the view and scaling of the graph can be changed with
mouse buttons 1 and 2. If additionally to these buttons the modifier <ctrl> is
hold down, the coordinate system only is rotated which is useful for large
data sets. A vertical motion of Button 2 with the shift key hold down changes
the `xyplane`.

Notice that the following will work:

echo "plot sin(x); pause mouse keypress" | gnuplot -persist

but this won't:

echo "plot sin(x)" | gnuplot -persist

since the gnuplot process must be alive for the gnuplot_x11 driver to talk to for the rotating.