Is it possible to see only the real path from the log without straight route lines?

I don't understand your question, could you perhaps illustrate with a screenshot?

I guess mikri means the magenta line for the planned route if you "Explore in Skydemon" an old track log.

Oh, I see. No; if you had a route planned for the flight then the plan will show as a faint magenta line in the background. As byom says, though, you can always export the flight log to view it in another app such as Google Earth.