The secularism and equality (homosexuality as well as women) isn't hard to understand, as one is directly from the Marx's views on religion, and the other a natural progression from both 18th century philosophers and Marx, once again, and early 20th century labour movements. The importance of 'stem' is harder, but I guess is to do with the left's belief in science and technological advancement which stems from Marx rather than any previous anti-indrustial socialists. However, of late the left is championing artistic subjects much more than the right. But I disagree with the claim that 'socialists' and anti-capitalists started in right-wing circles, when the 'left' began from revolutionary factions in France, no? The right were conservative and have mostly remained so, which in my mind means they could not have supported those causes.
Anyway, that's an argument that is never-ending. But I think the demise of the left in Europe is a theory that is slightly overblown. I agree with the lack of identity and direction, but I wouldn't ever consider "third-way" politicians to be social democrats or centre left. They are radical centrists, with (right) libertarian leanings. It just happens they rose in left of centre parties. Merkel is a good counter argument to this, her economic policies are very similar to Blair (probably further left) but she is in a nominally centre right party. But as a christian democrat she is less socially reformist. In Scandi countries the left parties are still doing pretty well, even if the Norwegian labour party just had a poor election (still biggest party, but were hoping for much more a year ago). The governing social democrats in sweden are comfortably ahead in polls, and in denmark the left-wing block is ahead. Spain's left is (properly) split for the first time in a long time, which is why PP always win. Italy only adopted an actual third way politician with the unelected Renzi, even if the previous PMs weren't exactly Berlinguer. France has an extreme blairite president, which shows those ideas are still popular (or more popular than le pen).
Basically, the article a year or two ago would have been much more apt than now. The centre left is undergoing a mini resurgence (and I am talking old fashioned social democracy, not blairism). After all, Blair's platform in his landslide 1997 was Corbyn's this year, just without the renationalisation and raised taxes. The same extra money promises. Portugal has seen a massive resurgence of the left, and in the UK it was basically a resurrection from presumed dead. The lack of identity comes from the hard left having a lack of moderity and fresh ideas, and centrist wings being happy with status quo. Nobody willing to take ownership and give new, innoviative ideas.