Russia has released a summary of the talking points they say the Taliban agreed to in the (earlier) July 9 talks. According to this, the Taliban have pledged to:
- not to breach Central Asian borders;
- to ensure all foreign diplomatic missions in Afghanistan are unharmed;
- to fight against the "Islamic State threat"; and
- to eradicate narcotic production (once the conflict is over).
The last point is probably not too coincidental, as Russia has [had] fair bit of a heroin problem; it was apparently top 1 consumer in 2010. Moscow occasionally declares the problem is bygone, but that's probably not quite that rosy in reality, and even if that's the case, a resurgence could well be enabled by the Taliban now [officially] controlling the border with neighboring states.
Russia has military bases in neighboring "buffer" countries, i.e. former Soviet republic and a defense treaty with Tajikistan where there is a large Russian base. To prove their resolve in keeping the Taliban out, Russian forces conducted maneuvers near the border this summer.
Before the Taliban were driven were driven from power in 2001, there was an active Islamist rebellion in
Uzbekistan as well, conducted by IMU. Apparently their remnants split in two factions, one of which pledged allegiance to ISIS (and the other to the Taliban),
which might explain why Russia is asking the Taliban to fight ISIS. ISIS itself has (or had) a small "branch" in Russia (Caucasus region).
Unlike China, Russia isn't as interested economically in Afghanistan, I gather. It's not too clear if they've offered any [economic] incentives to the Taliban. There's a recent FT article that discusses alleged Chinese promise to invest in Afghanistan, but nothing is said about Russia in that regard. Russia [openly] promised not to conduct airstrikes in Afghanistan (as long as the Taliban stick to their end of the "deal".)