This is a optional/invite only feature. LinkedIn doesn't provide that work email validation feature for all employers on their platform. Why did I know that? Because my past startup was requesting LinkedIn to enable that so that we can enable that feature but they said it's an invite only feature. Internally, I think they are only invite those employers who has certain amount of employees and/or revenues to turn it on.

Apple / Google developer program uses Dun&Bradstreet to verify company and developer identities. That's another way. But LinkedIn doesn't have that feature (yet).