Every table has a candidate key. (Possibly, all the columns.) Each value of that key designates something. If employee_ids weren't used externally, they and the the set of the other three columns would both identify sets of people with the same name, address and phone number.
You are right that a table must contain a natural key for whatever entity you want to identify--for "natural key" meaning "designator under the current business rules, external to the database".
You seem to be confusing multiple meanings for "surrogate key" and "natural key".
For "surrogate": One use is, a property set where designations are determined since current business rules: surrogate as new. Another use is, a property set where designations are determined since current business rules and only used internally: surrogate as internal.
For "natural": One use is, a property set designating under current business rules and before: natural as old. Another use is, a property set designating under current business rules: natural as external.
The original use of "surrogate" was as internal with "natural" as external. Unfortunately now usually people use "surrogate" as new and "natural" as old. And they seldom either consider or distinguish surrogates as internal. Some people might call a newly introduced external designator as both surrogate (as new) and natural (as external). (Re "meaningless" names.)
All you can do is decipher or ask what someone means when they use these terms.
Note that these definitions are relative to the "current" business rules. You also seem to be assuming that employee ids arrived with the database. At some point they were introduced, so were chosen after some older system started, so were surrogates as new under the new system. But if the database came later then by that time they were natural keys as old. They were natural as external both times; when introduced they were just new natural as external.