The forum databases do not contain payment information and are hosted separately from the game's servers. They do, however, contain the email addresses and passwords of forum users. The passwords are encrypted, though OP notes that many members "use weak passwords that could be guessed using brute force."
The company was unable to find "definitive proof" that game accounts were accessed in any way. In other words, it appears that payment information was not compromised. Any players who use the same password for both the game and the forums are advised to change them, along with any unrelated accounts or services that use the same email address and password.
OP has installed new security measures on both its forums database and The War Z's game servers.