As to being a viable method: while probably not economically viable I'm convinced it is technologically viable.
The tuned mass damper of Taipei 101 is designed to be not only functional, but to also serve as a tourist attraction. It seems to me that an energy harvesting tuned mass damper would be even more attractive.
The dampers are described as 'hydraulic viscous damper'. I assume that means that the dampers have a design similar to the shock absorbers of a car suspension system. Shock absorbers are filled with a viscous fluid, and when the piston slides in our out the fluid flows from one compartment to another though a relatively small hole. The friction of squeezing through the hole converts kinetic energy to heat.
To harvest energy rather than converting to heat a piston assembly would have to be designed to act as a double action pump. That is, it would have to have compartments and valves set up in such a way that sliding in and out continousely pumps fluid. The resulting flow must be run through turbines to convert the kinetic energy to electric energy. I have no doubt such a system can be designed.
For a system as large as the tuned mass damper of Taipei 101 the forces would be very large, meaning all the components of the energy harvesting system would need to be very strong, wich would make the system very costly. Adding to the cost: the system needs to be very reliable. General rule of engineering, the more moving parts, the more difficult it is to guarantee a very high level of reliability.
From an engineering point of view the passive tuned mass damper of the Taipei 101 building is probably the best design.