Thank you, I took the 64-bit installer from the archive page and now everything works fine

Yes, About Opera says "Windows 7 64-bit (WoW64)".
And the installer offered only "C:\Program Files (x86)\Opera" (which I accepted), not "C:\Program Files\Opera".
(I chose the "for all users on this computer" installer option.)
And yes, I used the network installer (file size only 1,07 MB (1.131.664 Bytes) in Windows Explorer file properties).
And I downloaded the installer directly from Opera.com (not via a software download portal).

Seems this is a bug in the network installer?

As a workaround, could you post a link where on Opera.com I can download the latest 64-bit stable version?

@Chromium: I guess Chromium will prioritize their 64 bit version, because Google Chrome by default installs its 64-bit version on Windows 64-bit systems (tried yesterday on the same computer).

It seems that the current Opera installer (42.0.2393.94 just downloaded from Opera.com) always installs Opera-32bit, even on Windows-64bit. What is the reason for this behaviour?

I would prefer Opera-64bit for enhanced security, such as Windows support for DEP (Data execution prevention).
Where on Opera.com can I download this? Will security patches be released always at the same day in Opera 32-bit and Opera 64-bit, or may Opera-64bit lag behind?