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No, the win-lose record actually doesn't imply what you think it implies, and this is the central flaw in Devereaux' argument.
A "batting average" in a sports league works because two conditions are met:
In battle, neither of those are true. Various methods of gaining an advantage like bringing more numbers, occupying a good position, attacking enemy logistics, launching a surprise attack and various other stratagems are commonplace. The "quality" of the soldiers is only one factor in many deciding the outcome of the battle.
Secondly, a general can choose to decline battle. As Devereaux himself detailed in his series on gneralship, battle normally only happens when both generals think they have a reasonable chance of winning (although there are ways for a good general to try forcing a battle anyway).
What does this mean? It means unless there's a consistent skew in the judgment of the generals, the expected outcome in a battle, and therefore the expected win-loss-ratio of a faction, will be 50:50, no matter the relative quality of the soldiers!
If one side is reputed have the better soldiers, then the other general will decline a "fair fight" and instead only offer battle if he believes he has a way to make up for it. Maybe he waits for reinforcements to gain a numbers advantage or occupies a advantageous position like a hill. Meanwhile the spartan general might see those odds but believe the valor of his men may carry the day anyway. So battle will be given once the odds are, on average, equal, after accounting for the soldiers' skill. A stronger faction will not win through winning more battles, but through having more ability to give battle, for example by simply marching up and giving siege, without the enemy ever seeing an opportunity to stop you. And if the mismatch is too great, the weaker side will consider sueing for peace rather instead of going to war at all.
So, with that in mind, what does the mediocre win-loss ratio of spartans tell us? It tells us that the reputation of spartan hoplites was more or less accurate! If they were consistently overestimated, then we'd see a streak of losses for Sparta, as overly cautious enemy generals would stack advantages before they dared to give battle, and overly confident spartan generals would happily accept those bad odds because they believed their troops could handle it, and then the reality of the stacked deck would assert itself. Of course, such a losing streak would rapidly tank the spartan reputation, allowing the perception to realign itself with reality, at which point the win ratio levels again.
So, the conclusion from the data would be the opposite of what you and Devereaux think. The elite reputation was deserved, and Sparta gained influence by winning wars because they could offer battle where others could not, or simply by bullying their neighbors into concession with the threat of their army. And if they overdo it, their neighbors start allying against them, thus gaining a numbers advantage to cancel out individual prowess.
(The alternate explanation would be that spartan generals were consistently superior, and everyone falsely attributed their success to their troops, but I don't think I've ever seen anyone claim that.)
And to be clear, this doesn't mean Spartiates were supersoldiers. But it does appear as if they were at least noticably better than their peers.
It also doesn't mean the "300" memes are accurate, because it doesn't tell us where their advantages lay. Maybe it's simply the better maneuverability and tactical flexibility Devereaux mentions, or any other martial virtue.
One last thing to consider, an elite reputation, even if (mostly) undeserved, is itself a material asset. If everyone believes Spartans are invincible supersoldiers, this will boost their morale and drop their enemies' just from the prospect of fighting them, and morale decides battles. This could even become a self-fulfilling prophecy. But that doesn't change the conclusion. An average win ratio means at least the generals know how good they are.
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