How to obtain reactant lifetime using transition state theory?
As far as I understand, there are two things that I should answer for you.

Calculating rate constants with any trajectory methods is different than using TST. In fact, the whole point of using QCT is so we can account for nonstatistical effects. These nonstatistical effects are usually extremely important, as it is also mentioned in the article 


  ... This dynamic matching leads to pronounced nonstatistical effects
  on the lifetimes...


Any time you are using TST, you are assuming there are no nonstatistical effects whatsoever. This approximation is probably never true, but it leads to surprisingly good numerical results. The way you calculate reaction rates in QCT is by integrating the reaction probability using a Monte Carlo integration formula, cleverly sampling the initial conditions of the reactants. I usually recommend a good book of W. Miller. The book itself is a bit outdated, but the derivation by Porter and Raff in the first chapter is beautiful.

Now you asked about the determination of the lifetime. The article, as I understand it, talks mostly about the lifetime of the activated complex. This can be done because in QCT we know the coordinates of atoms in every single timestep, so we can compare them to some given values to decide whether we are in the activated complex region or not. From the article:


  Transition zones were defined for the C–C forming (3‡) and the C–N breaking (5‡) steps (see Supporting Information for details). [...] The lifetime of 
   intermediate 4b was defined as the elapsed time between departure from the transition zone 3b‡ and entrance in transition zones 5b‡ 


So, long story short: QCT determines lifetimes differently from TST, this is because TST is inherently statistical, while QCT also considers nonstatistical effects. Instead, QCT calculations rely on defining geometries for different states, and simply calculating how many integration steps the system spends there.