This problem has a very simple solution, but it comes from laying out a premise of what "skill" is. In DPP, with the enormous number of threats in addition to various Pokemon being able to threaten in many different ways (see Tyranitar, Salamence, Lucario, and Latias to name a few), I feel that battle prowess is demonstrated not by 1 on 1 battles, but specifically how a battler and his team manage to handle various teams over a long period of time.
That's "skill" regarding the overall metagame. But this topic is talking about "skill" in battle, and I hope that you'll see that this idea of long term management applies once again.
A lot of you seem to be separating "skill" and glorified guesswork; I ask "why" Glorified guesswork as a phrase obviously has negative connotations, so I'll use assumptions based on information gleaned in battle, and influenced by time in battle. "Predicting" your opponent will never be a 100% art; that much, I hope is obvious. Since it cannot be 100%, I hope you can see that "prediction" as a "skill" then becomes how close you can get to 100%. In this sense, your ability to make guesses is a skill in itself. So the "simple solution" I talked about is that predictions are a result of skill, which is the skill of making educated guesses. Of course, I will also show cases where in spite of any and all efforts, a "prediction" is merely "glorified guesswork." Note that this is situational, and just because there are some situations where a prediction might not be more than an arbitrary guess, that doesn't mean prediction isn't a skill.
I'll describe a bit by what I mean by information gleaned in battle. This has various aspects, but the most obvious is first "in simple terms, what is the skill level of your opponent" If he, in the early game, is pulling all obvious moves, you can use this information to turn a 50-50 switch into a confident "he is most likely to do this" switch. If your opponent is skilled, this becomes much more complicated, and ironically, more guesswork than before. 2 skilled players will know that the other is skilled, and will know that the other is capable of making a clever switch. This, of course, introduces a back and forth mindgame of various degrees which eventually leaves knowledge of style almost meaningless. That's why, if you'll notice, so many high level matches in DPP turn out to be influenced by team matchup (and which is why many of us are pulling for Bo3 tourmaments to reduce the effects of team matchups). So, in terms of using opponent's skill level as information, this works best against players with a tendency for the "Safe" or "obvious" play; as you face more skillful players willing to take risks, this becomes more and more guesswork. Of course, to reduce the unfortunate direction back in the "glorified guesswork" direction, you use the next (second) available information: opponent's team.
General knowledge of team type and pokemon teammate trends along with whatever 3,4, or 5 pokemon are revealed can allow you to make educated guesses regarding what is left over and what he might do. This specifically is paramount in the "long term thinking" factor that you'll see many good advance players talking about. If you "predict" that a Latias is the last pokemon on a team, the skillful move would be to reduce risky situations for your Latias counters, and make moves with the knowledge that your opponent has a Latias waiting in the wings. This doesn't have to be a specific Pokemon; for example, if you are facing an offensive team and note that the opponent hasn't used a Steel like scizor / salamence / metagross yet, you can "predict" with your own Salamence in spite of not definitely knowing that he has it. Knowledge of team also helps reduce guesswork among 2 skilled players against each other; regardless of how 2 players would choose a move depending on playstyles, teams and team strategies inevitably influence a player towards certain tendencies, and a skilled player will be able to recognize this.
A third example and the final I'll bother wasting your time with lol is very closely related to the first 2 (in fact some might argue that it is just a subset one of the first 2) and quite "obvious." That is the information that YOU have given to your opponent, both regarding your own skill and regarding your team, but more your own team. Depending on what strategy your team has shown the opponent and what Pokemon have been revealed, you can further reduce the "pure guesswork" or "arbitrary" aspect of a "prediction."
Going back to my "I'll use assumptions based on information gleaned in battle, and influenced by time in battle," you'll notice I mention time in battle. This is referring to, in very rough terms, the early, mid, and late games. In the early game, with an offensive against a defensive Pokemon, it is generally advisable for the defensive Pokemon side to "use the safe play" because at this time in the battle, your ability to reduce the arbitrary nature of a guess is significantly low and as a defensive Pokemon it's general job is to be at high health. For the offensive Pokemon, it is generally advisable for a "random play," because the defensive Pokemon will rarely be able to significantly damage the offensive. Where this becomes problematic in the early game is when an offensive pokemon and an offensive pokemon are pitted against each other. With little information readily available, this once again boils down to a back and forth of mindgames of various degrees until a "prediction" is a random move, and unlike the offensive pokemon vs. defensive pokemon, not a random move of "skill." Again, this tends to boil down to how effectively a person has built his team and team matchup rather than prediction skill. The mid to late games, however, provide an opportunity for a user to use all of the information he has gathered and assumed to try his best to reduce the arbitrary nature of a guess as much as he can.
So basically, if you recognize that battle prowess in DPP is how a battler and his team do over a long period of time against various teams ("threat management" + "ability to successfully accomplish a strategy"), you can make the argument that "skill" in specific battles is using as much information available from assumptions on opponent skill, opponent team, and information given to the opponent + appropriate knowledge of the time in battle to reduce the arbitrary nature of a guess as much as possible.
So to answer this thread...of course prediction is a skill