*sigh*
No, men are not finished. Here's a good example of why: take a decent look at the boards of the largest companies, the governments of nations the world over, the various national military commands of developed countries and even their judiciaries. In other words, look at the people who wield the most power in the world. You'll be lucky to find more than 10% of that group being female.
Yes, women have made great strides in the last 50 years - to the point where, all other things being equal, men and women have similar levels of opportunity in most of the Western world. Yes, that is a challenge to the old order of things, where men were the breadwinners and women were the housekeepers. Yes, the successes of feminism and affirmative action have left a gaping wound in the "traditional" male psyche, which I think is one of the greatest condemnations which can be levelled at first- and second-wave feminism (i.e. it's not good enough to simply come in and tear the house down in the name of a higher morality if you offer nothing to replace it). Yes, the introductory statement of that Slate article/debate is misleading - how about mentioning that gender stereotyping is arguably one of the main reasons why so many men are in prison and thus themselves victims of patriarchal social relations (itself indicative of the continued power of existing social structures)? Presumably, observations like that just didn't fit the meta-narrative of scaring insecure people who fear change.
As things stand, men aren't "finished", and anyone who tells you otherwise is either panicking, trying to sell you something, or fundamentally misunderstands the world.