It "benefits" the enemy - but remember that they basically have to play the card the turn they get it, or it gets really out of hand really fast. At 2 mana, it's an incredible on-curve tempo play.
I don't think you're quite taking into account the value of forcing a specific play. 1 mana for 1 damage is good, yes - but unless they're a ping class it's not going to often kill this creature - and even if they are, you've often forced their turn 3 to entirely be killing the plaguemaster, and you maintain tempo. This card, as is, would be the best tempo play in the game.
I do like the idea of the card overall, but the plague as-is is incredibly problematic. There are a lot of ways to fix it, I think, but with the current text you basically have three options:
Spend 2 mana the turn you get it to get rid of it and deal 1 damage. If plague master was played on curve, you have either 1 (on turn 3) or 2 (on turn 4) mana left to make a play of your own, and you're not even guaranteed to deal with the plague master body.
Play something else on curve, and spend 4 mana the next turn to clear the two plagues you now have in hand and deal 2 damage. This lets you have a turn 3 (or 4), but completely kills your turn 4 (or 5). You default to option 3 if the opponent plays a second plague master at this point, and are basically forced to leave at least one minion they have on board alive since the 2 damage + your 3 drop is unlikely to be able to kill their 3/2 + their 4 drop.
Never draw a card for the rest of the game. You get maybe three more cards - but after the third turn, you have eight of these in hand, and it's functionally impossible to get rid of them all - and if you have at least 5 in hand at the end of the turn, your hand fills with them, and you miss next turn's draw. Every non-plague card you play gets replaced by a plague at the end of the turn. Every plague card you play also gets replaced by a plague at the end of the turn. You probably just eventually lose the game, or are reduced to dealing damage to creatures/face at a 1 damage per 2 mana ratio.
The general problem is that all three of these effects are incredibly bad for the player who has to deal with it - and the player who caused it basically spent only one extra mana to do so (getting a 2 mana body on a 3 mana card). The body either needs to be much worse for the mana cost (i.e., has one health so it dies to its own plague, 3/2 for 4 mana so you at least eat the same 'cost' the opponent does, etc), the plague needs to be easier to clear from hand, or the plague needs to spread a whole lot less virulently.