Using restrictive appositives with possessives correctly

a) After three years of speculation, James McAvoy has confirmed that he’s quietly tied the knot with partner Lisa Liberati.

b) James McAvoy has confirmed that he secretly married his American partner, Lisa Liberati.

The sentence from b) is from The Independent and a) is Evoke.

Two sentences on the same subject structured slightly differently.

Here is an example from the New York Times article on correct comma usage: https://archive.nytimes.com/opinionator.blogs.nytimes.com/2012/05/21/the-most-comma-mistakes/#:~:text=The%20basic%20idea%20is%20that%20if%20the%20name,the%20sentence%29.%20If%20not%2C%20don%E2%80%99t%20use%20any%20commas.

My son, John, is awesome. (If you have just one son.)

But withhold the comma if not unique:

***My son John is awesome. (If you have more than one son.)

The only difference in the examples a) and b) is the possessive 'his' and that seems to have governed the usage of a comma?

With or without the possessive his, doesn't the example show a unique person and therefore the usage should be non-restrictive appositive and require a comma strictly speaking?

When an identifier describes a unique person or thing and is preceded by “the” or a possessive, use a comma:

Baseball’s home run leader, Barry Bonds, will be eligible for the Hall of Fame next year.

A restrictive appositive identifies a noun, so it is never offset by a comma (or a pair of parenthetical commas if it doesn't appear at the end of a sentence) because the information it conveys is essential, not parenthetical.

What is "essential" information can be subjective, and that is why both of your examples are fine. In example 1, it could be argued that "his American partner" is essential information because the reader may not know who Lisa Liberati is. James McAvoy is considered an "A-List" actor; his wife is primarily known as a production assistant. But, in example 2, the information that he married his "American partner" comes first. As she is not particularly well-known, her name has been added parenthetically.

So, example one uses a restrictive appositive; example two adds the same information parenthetically.