Update:

Took my bike inside to inspect it, and the first thing I saw was that the rear wheel was not in the center. I use dropout screws to fixate the rear wheel and seems I pushed them too far towards the edge of the dropout, and the left one was not same length as the right one, it was screwed more than the right one so it seems that when I first applied alot of pressure, the rear wheel "aligned" next to the screws - that is - left the center and therefor made possible for chain to skip the rear cogs when using a lot of power, since the rear cassette in this way - was not parallel with the front cogs. I did remove the chain and cleaned it, just for the sake of doing something to dirty my hands. Aligned the rear wheel a bit deeper in the dropout and made sure the dropout screws are now the same length. Also I tightened the right down tube shifter a bit, just to be sure.

Tried sprinting on my way back from work a minute ago, and did not experience "ghost shifting", and I did not notice the derailer move at all, so it seems I fixed the problem, and blamed the bike for my error!

Though I will definitely get a new chain in a couple of months, I'm using the old one from the 6 speed cassette, it works and doesn't scratches the adjacent bigger cog, but just to be on the safe side of having the right stuff on the bike.

Hope to do a local mountain climb on sunday, there I will use more power than usually commuting, so I'll know if the ghost shifting problem is definitely fixed.