Can PuTTY open SSH link similar to Terminal for Macintosh?

PuTTY unfortunately does not associate itself with the ssh:// URLs.

You can associate an application with a protocol manually. See the MSDN article Registering an Application to a URI Scheme.

Basically you add a registry key like:

[HKEY_CLASSES_ROOT\ssh]
@="URL: SSH Protocol"
"URL Protocol"=""

[HKEY_CLASSES_ROOT\ssh\DefaultIcon]
@="\"C:\\Program Files (x86)\\PuTTY\\PuTTY.exe\",0"

[HKEY_CLASSES_ROOT\ssh\shell]

[HKEY_CLASSES_ROOT\ssh\shell\open]

[HKEY_CLASSES_ROOT\ssh\shell\open\command]
@="\"C:\\Program Files (x86)\\PuTTY\\PuTTY.exe\""

Though the above passes a whole URL to the PuTTY command-line. And PuTTY does not understand the ssh:// prefix. So you would have to add a wrapper script that strips the ssh:// and passes only a user and a host to PuTTY.

For that see:
https://johnsofteng.wordpress.com/2009/05/12/launch-putty-from-browser/

I do not know 1Password, but a similar application KeePass can parse the URL and pass only its certain parts to the application. So it can strip the ssh:// for you.

See KeePass override rules.

On Windows, WinSCP 5.9 and newer registers itself to handle the ssh:// URL and opens the session specified by the URL in PuTTY.

(I'm the author of WinSCP)