Targeting of G-quadruplex (G-Q) nucleic acids, which are helical four-stranded structures formed from guanine-rich nucleic acid sequences, has emerged in recent years as an appealing opportunity for drug intervention in anticancer therapy. Small-molecule drugs can stabilize quadruplex structures, promoting selective downregulation of gene expression and telomerase inhibition and also activating DNA damage responses. Thus, rational design of small molecular ligands able to selectively interact with and stabilize G-Q structures is a promising strategy for developing potent anti-cancer drugs with selective toxicity towards cancer cells over normal ones. Here, the outcomes of a thorough computational investigation of a recently synthesized monofunctional PtII complex (Pt1), whose selectivity for G-Q is activated by what is called adaptive binding, are reported. Quantum mechanics and molecular dynamics calculations have been employed for studying the classical key steps of the mechanism of action of PtII complexes, the conversion of the non-charged and non-planar Pt1 complex into a planar and charged PtII (Pt2) complex able to play the role of a G-Q binder and, finally, the interaction of Pt2 with G-Q. The information obtained from such an investigation allows us to rationalize the behavior of the novel PtII complex proposed to be activated by adaptive binding toward selective interaction with G-Q or similar molecules and can be exploited for designing ligands with more effective recognition ability toward G-quadruplex DNA.