I think the threat's definitely there. Facebook wants to eat everyone's lunch, and they're basically knocking on doors in LinkedIn's neighborhood.
LinkedIn can be described at the 'Facebook for business', it doesn't feel like a stretch that faceboook might someday want to become the facebook for business.
FB for Work looks like a competitor for Yammer i.e. an internal social network for companies offering internal communication with notes, status updates, etc...
LinkedIn is primarily used to professional networking outside your company. Keeping in touch with ex-colleagues, recruiting, sharing industry-specific posts, etc.
Facebook at Work is aimed at internal networking, so communication among large teams, company news / communication, etc.