Employer Identification Numbers are used for taxation purposes. In the USA, they're used for when employees file their Federal and State tax returns, as well as for what taxes are determined to be owed to the federal government by the agency itself, as well as what rebates and credits the business is entitled to (there's a lot of these). If a business lacks one, it's not entitled to tax benefits, and, if it brings in enough income to be worthy of note, it can face penalties including fines. It's not a massive deal, business goes on that isn't properly legally backed up all the fucking time, but it can definitely explain why Wu's reputation with her employers is shit - she worked them off-the-books, which means they weren't entitled to benefits when they fucked off from Chateau de Wu and likely had no real job security.
No wonder Wu gets along so well with the Gawker supporters; they treat their employees the same.
@Yellow Yam Scam elaborates:
All of which brings me to this:
....Someone, please look into this. Wu will be fucking
apoplectic.