Final answer:
The network model described is the client-server model, where specialized servers provide services to client devices on an enterprise network.
Step-by-step explanation:
The type of network model that requires the use of specialized computers with networking operating systems to provide services to other devices over an enterprise network is the client-server model. This model is structured with servers that offer services such as data storage, email, or web pages, and clients that request these services. The client-server model is distinguished from other models like peer-to-peer, where devices share resources among themselves without centralized servers, or point-to-point and hub-and-spoke models that pertain more to the connections between nodes rather than the distribution of services.