UPDATE
Steam appears to launch only from the terminal, not from the menu or a desktop icon. But, remember, reboot first before trying to launch it, because if it fails to run, it won't ever run again even from the terminal, this is most confusing. So, I hope to help at least somewhat. Will be updating if I find a better solution.
Editing the .desktop file, and commenting out these two lines, also did the trick, at least it seems:
#PrefersNonDefaultGPU=true
#X-KDE-RunOnDiscreteGpu=true
I wondered why a simple downgrade did not do the job. First, version 530 is somehow treated the same as version 535, so you need to downgrade to version 525.
Then reboot and upgrade back to version 535. But beware, there is some glitch, at least on my laptop, which causes my machine with this version to go into a black screen. Note: This issue when running the install command below is of no problem, wait a moment 15 minutes, for example, more info in my answer here:
How to install the latest Nvidia drivers on Linux Mint
Press the power button once briefly, it should safely power down your machine even if the screen was black. Tested.
Note: Always install the driver with the generic command like in the above answer, snippet:
sudo apt-get install --install-recommends nvidia-driver-535
(I prefer to avoid using any GUI driver managers as I said in the above answer.)