The email Namecheap sends out is very shady looking. I had to google around quite a bit before concluding it was genuine. The verification link leads to the domain raa.name-services.com and is not delivered over https. It looks exactly like I imagine a targeted phishing email to look.
That's the same domain they use in the e-mail you get asking you to review the accuracy of your WHOIS data. They send that e-mail for every domain you own, every year, as required by ICANN. For Namecheap customers, the domain should be familiar, after the first mail at least.
The subject line of those mails is: Important Notice Regarding Your Domain Name(s)
The new mails have a stronger subject line: IMMEDIATE VERIFICATION required for [domain]
It's not Namecheap sending those out: Namecheap is simply an eNom reseller and the email you received was likely directly from eNom, with some Namecheap branding attached. *.name-services.com is used for various eNom-related stuff.