That doesn't make sense, Malfurion was the first druid and for 10k years until after wc3, only elves were druids...this is why I say druidsm in wow is an elven thing (for all you newer players, and I mean newer as in joined warcraft after wow and likely after wotlk). Malfurion developed Cenarius' teachings to the level that was high enough to be a class of it's own.
If you know your lore also, Cenarius involves himself with the night elves shortly after their creation, these arcane elves show a benevolent love for life and nature with an intelligence that so stands out, forest spirits spread words of their deeds to the demi gods on Hyjal and Cenarius their greatest physically reveals himself and teaches them.
When their arcane love grows so strong many stop following the forest ways (it's not druidsm yet) he leaves them (knowing he isn't getting through any longer I.e, appreciated is the implication), this is when he goes and starts hunting with the tauren, teaching early tauren some of his things (and where the early tauren druid connection comes in, but it's still not developed into what would later become druidsm at this point - but we use the name so you know what field this is).
So night elves first, then tauren.
However the tauren wander off too, (though unlike the night elves, I reckon they still revered him), and by the time when he is now a legend myth amongst the night elves just before the first demons arrive 10k years ago, Malfurion finds him searching for his calling and a way to save his people who in their arcane obsession had lost their souls (read WotA; The Well of Eternity) . Together with Malfurion, the story of the war of the Ancients continues and Malfurion wins the war, Cenarius continues teaching him and he develops his Shandos earlier teachings into what becomes druidsm, the night elves make a pact with the green dragonflight to work in evolving the world through the dreams, most of the male night elves who were Moonguard and highborne not loyal to Darth'remar switch to druidsm because of the need to ban the practice of arcane. The art/craft develops a sophistication pretty much like night elven society developed the arcane into the levels that 10k years later wc3 mages still hadn't come close to.
Only night elves are druids at this point until Malfurion teaches Hamul Runtetotem after Wc3 and we get tauren druids. If you were involved with warcraft in the early 00s you would know only night elves were druids and only Male night elves. Chris Metzen wanted to keep this for the game but his colleagues at blizzard wanted no gender differences, and wanted the factions to have the same classes, eventually, both druids and warlocks became a thing for both factions with the other devs barely accepting that Paladin and shaman should be unique too the factions which later changed in TBC.
Interviews revealed this. It is my opinion that Chris Metzen has not been the same concerning warcraft since then, I believe he became less influential and motivated after being undermined and over ruled on these issues (my opinion here), I think seeing his colleagues unwilling to protect and value the lore and uphold its integrity hurt the sensitive guy big time, and from a lore perspective, many of the gameplay changes like 2 factions, instead of 4, female and tauren druids, alliance warlocks, male night elf priests were criticised. But wow was so successful, no one cared at blizzard ( my opinion because nothing changed) I assume developers became vindicated in their choice when the great arguments of alliance advantage with Paladin or horde advantage with shaman sparked flame wars all over the official boards.
By TBC, they opened up both classes to the opposite faction.
But to answer your question, no, druidsm was an elven thing at first.
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I just noticed, I was busy typing another response, that then turned into a mini essay which I just posted, then noticed all the stupid typos. Will edit
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Night elf shenanigans? You have no respect for your elders do you, these are 10k yar old + people who formed and developed the arts of magecraft, druidsm, demon hunting from arcane, nature and fel studies to the greatest extents in warcraft lore.
Night elven shenanigans indeed - when it ccomes to mages, druids, demon hunting show some respect, and these are no novice hunters and preists either, they are the most long lived and well practiced/developed in all these of all the Azerothian native races. You youngster punks these days... that's the problem with humans and orcs, they get a few successes at things and now they thing they are unrivalled masters of all. pfft