I found out what is happening:
It looks like I had to download another file, run it, then extract, another file, and overwrite some of the downloaded files.
I do not understand why do we have to do this nonsense manually, and why Intel did not bother to explain this in the Quartus II download page.
Anyway, the info is here:
https://www.intel.com/content/altera-www/global/en_us/index/support/support-resources/knowledge-base/tools/2019/why-does-the-nios--ii-not-installed-after-full-installation-of-t.html
Eclipse now launches OK.
Case is resolved.