Yes, it's a phishing email but where it's different and vulnerable is that you receive a seemingly legitimate email from LinkedIn (it's in fact a legitimate email that was "forwarded" to you), that
does link to LinkedIn.com, not limkedin.com or similar. You never actually give your email and password to a site that makes you think it's LinkedIn. It IS LinkedIn.
The weak part is that your LinkedIn account gets associated to an extra email address without your express consent. (allegedly, since I haven't tried this)