As far as I know, the BTC-e servers are in russia, US can't have taken them and so I don't think they have any private keys at all (maybe only Alexanders one from his phone).
So could it be this ETH move is done by the BTC-e admins for their new website???
It is possible. They moved out 0.0001 ETH and then in 0.0001 from clearly someones private ETH wallet, because there is poloniex transfers.
It can be a troll sending back the 0.0001 ETH from another ETH account because he seeing action on the BTC-e ETH wallet and wants to stirr up more shit right?