The discussion itself will go nowhere, as there are not clearly defined terms that everyone is expected to use.
For instance, what do you MEAN by "skill?" What is the definition, or at the very least DESCRIPTION of what constitutes "skill?" Is this physical skill (like reflexes, endurance, or hand-eye coordination)? Is this mental skill (intelligence, knowledge, memorization, or reaction speed)?
Different genres highlight different aspects of the "skills" I just listed. Some, however, might not consider "memorization" to be very skillful--which would leave out a big portion of the "skill" in fighting games, which revolve around memorizing special moves and combos. Others might discredit reflexes, as some of that can be attributed to a disparity in hardware or software effectiveness between opponents.
Basically, there are two camps showing the most here:
Camp A, in which "skill" is largely physical. They tend to favor FPS and fighting games, citing that a person has to have good reflexes and muscle memory. The other camp will simply claim it's all rote memorization (of combos and character-specific strategies), and isn't inherently skillful.
Camp B, in which "skill" is largely mental. They tend to favor RTS games (and, to a lesser degree, also fighting games), citing that a person has to know the tools they have, when to build what, what to use where, and be able to react to any opponent on-the-fly. The other camp will simply claim it's all about rote memorization (of the units and their foils), and isn't inherently skillful.
In both cases, people will claim that the game requires skill because playing against a human opponent means an infinite number of possible strategies with which to contend. And, when the opposing side makes the same argument, both camps will claim that while it's POSSIBLE to have infinite strategies, there inevitably arise two or three that everyone uses--the ones that distill the game mechanics down to the lowest-common-denominators (offense, defense, and speed, usually).
