Follow-up:
It seems like open.vm-tools were installed but still the copy-pasting did not work.
So I did this after reading another thread concerning the tools and linux Mint:
sudo apt-get update
sudo apt-get remove --purge open-vm-tools
Then inside the ~/vmware-tools-distrib folder I did this:
sudo ./vmware-install.pl (followed all the prompts)
/usr/bin/vmware-user (instead of logging off and back on)
Now my guest has copy-paste both ways.
Why does VMWare recommend to use open-vm-tools when it so obviously does not work?