As usual, this type of magazine article is talking nonsense. I quote:
"The decision means that, should Earl Spencer remarry, his fourth wife
would carry the title ‘the Countess Spencer’, while Karen would be
referred to as ‘Countess Spencer’."
The distinction between a divorced wife of a peer and his new wife is actually that the former wife places her forename before her title, i.e. "Karen, Countess Spencer". However, as Debrett's says, "In the event of a divorced peer remaining unmarried there is no reason
why his former wife should not continue to use her title without the
qualification of her forename."
The use of the definite article with peerage titles is a rather formal form. As rcb1 says, it is only correctly used with a substantive title, not a courtesy title. If The Earl Spencer remarries, his new wife could be referred to either as Countess Spencer, or more formally, The Countess Spencer. The inclusion or omission of the definite article is not what denotes her marital status.