For a long time, there wasn't an installer for putty, so a lot of us became accustomed to just dropping the binary on our desktop or "bin" folder", but there is an installer now. Also, certain corporate environments that preclude the installer from working correctly, but won't mind you "installing" a program to your desktop/local app data.
I find the corporate environment thing suspicious. I could imagine that if you don't have admin access, you can't install to Program Files, but couldn't you still install to your home directory, and still get those lovely start menu shortcuts?
Windows, by default requests elevated rights from the user (the UAC dialog) if you run any exe that has 'setup' or 'install' in the name, or if the manifest inside/alongside the exe defines a requirement for elevated rights.
You can spot these files as they have a little Windows 'shield' overlay on their icons (Windows overlays that itself if it detects a file needing elevated rights).
So, unless you can elevate your rights (i.e. be admin, or type in admin credentials), you can't run most installers.
However, prior to Windows 7 your personal start menu folder wasn't locked down - and as a non-admin you could easily add/remove shortcuts from it. Since Windows 7 onwards it's now protected, so you need to elevate to be able to write to it.
Windows allows you to run (by default) software from ANY folder you like, but you can only (by default, again) write to some of your user folders and the the %TEMP% location.
So downloading the PuTTY exe and running it from the downloads folder or desktop is perfectly legitimate, although not good practice.
As an aside: I'm not sure if Chrome still does it, but I recall that if you try to install it and you don't have admin rights, it just puts an icon on your desktop, and installs all the chrome files into a folder under ProgramData which resides in your user hierarchy, instead of the locked down Program Files area. Which is one way of getting around the lack of admin-rights.
