Software to model and analyse protein–ligand interactions
I don't know precisely what you mean by "analyze", which could be anything from simply "view" or "measure distances", to evaluating an energy function on a crystal structure or molecular dynamics simulation, to prediction of binding sites de novo. The tools are different for each case, though some can do several things.

For simply viewing, measuring distances, and creating "pretty pictures" like the ones you included with the question, PyMOL and UCSF Chimera are the most popular tools. Chimera is highly scriptable and can perform molecular dynamics simulations (i.e. simulate movement of atoms based on an energy function), though its capability in this regard is somewhat limited. The NAMD/VMD software suite (which was used in the study cited in the question) is more full-featured, as is CHARMM (the latter of which is also the name of an energy function). For prediction of binding sites de novo (without a bound experimental structure), i.e. "docking", there are DOCK and AutoDock (both with long academic histories) as well as more industry-oriented ones like Glide.

Be careful though what you're getting into — while simply viewing structures and making geometric statements by direct observation is well within reach of the average biochemist with reasonable knowledge of protein structure (provided you trust the lab that solved the structure in the first place!), simulation of proteins using energy functions requires considerable computational expertise, though the "black box" nature of some software glosses over this. It may be relatively easy to run a simulation using questionably appropriate parameters, but the adage "garbage in garbage out" applies very much here. This is somewhat true with docking as well.