I can confirm that this person named Bii
zzard does not work for us.
Real Game Masters have a Blizzard icon next to their names and the chat itself takes place in a separate chat window.https://us.battle.net/support/en/article/game-master-interaction-policy
To learn more about account security and types of account thefts, check out this support article.http://us.battle.net/en/security/theft#phishing
[Edit]: And for the sake of thoroughness, under no circumstances should anyone try to visit the website in the OP's screenshot. It could be malicious(that's bad.)