It's hard to believe that it's an exchange since just buy and don't sell. And keep buying 69 doges and 420 doges as a joke.
You can't tell that transfers into an address are done with the consent of the address owner at all, or that they represent "buying". The only activity that is provably initiated by the address owner are the transfers out, and none of those are meme amounts. In fact they're all to a single wallet. Probably the exchange's hot wallet.