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.