Well the author has a somewhat saner idea then most people are feargasming about, apparently he is someone that has actually been there and knows what is going on, but those 4 points are not perfectly accurate.
1) Aside from a sense of poetic justice, the actions of the 1980 war does not form a basis for modern Russian actions. Far too much at stake for this to be about revenge.
2) This is the relevant point many people seem to miss. Russia has been directly helping the Taliban for a very long time. The quantity of support did not change, what is happening here is that they are making aide contingent on violating the peace agreement. It is in Russia's best interest to keep the conflict going.
3) As I have mentioned before the "Taliban" is not any sort of actual organization in the way we think of it. The last leader of the whole Taliban was Mullah Omar, who apparently died in 2013, but remained the "Leader" for another 5 years, even after it was fairly obvious to everyone he was dead. One element of the Taliban turning down the offer has not influence on another cell accepting it. Russia is not negotiating with the "leadership" in Pakistan here, they are negotiating with local leaders on the ground.
A (Very) oversimplified breakdown of what the Taliban is now:
a) Pakistan based leadership cells, or "Shuras". The two most influential are the Quetta Shura and the Peshawar Shura, named for the cities they meet in. These are not really operational leadership cells like a military HQ, they are counsels of Islamic Scholars and Clergy that issue Fatwahs and religious guidance. They are constantly requesting resources and issuing general directions, but nobody actually reports to them directly. These are what the US negotiated with.
b) Foreign militarist fighters. These are loosely speaking Jihadist gangs. They come from all over the Muslim world to fight in Afghanistan. The most numerous are groups of Arabs and Chechnyans, but many other groups exist as well. They are usually better equipped, and occasionally better organized. They typically follow a charismatic leader of that group, who may or may not care what the Taliban Shuras say.
c) Local community leaders. These are the village elders and warlords that care for their family and communities interest. They tend to change allegiances as often as necessary to survive. The are the people in Afghanistan that the Shuras are generally talking too, and they are by far the most common and active of the "Taliban". Most of them are willing to coexist with anyone that has sufficient military power. If the Coalition military has a large enough presence in the area to be the dominate force, these guys will happily be loyal to the afghan government. If IS shows up, they become IS, etc. They are surivors and opportunists mostly focused on caring for their people.
d) "Ronin". These are disposed young Afghan men, mostly from refugee families. They tend to move around, living on the charity of Local Taliban leaders and following the religious guidance of the Shura. They are expendable, and the easiest force to move around and mobilize.
e) The Drug Lords. Dominated by the loose Criminal Syndicate of the Haqqani network, which is as the name suggests, a network more than a solid organization. These are profiteers, business tycoons, and drug peddlers. Extremely wealthy, well connected, and pragmatic. Basically no religious motives here, pure money and power.