They are watching DHCP Discover option 55. The device tells the server what options it expects to receive, and different vendors and device ask for different options or ask for them in a different order, and they are fingerprinting that.
Cisco also describes the tactic: https://www.cisco.com/c/en/us/support/docs/security/identity-services-engine/116235-configure-ise-00.html
The fingerprints are viewable at https://github.com/karottc/fingerbank/blob/master/dhcp_fingerprints.conf - it is more specific than a mac vendor but not extremely anti-privacy, anybody watching firewall logs will know an iPhone connected pretty easily too.