You may also use likeness or resemblance instead of identification with.

“To identify with” is a vague phrase. It is generally used to mean that a person feels that they are part of something or some group, and that group/thing is important to them. Here, it appears to mean that some people (student, alumni) have very strong positive feelings about athletic programs at their school. They feel good when “their team” wins. The athletic programs help build school spirit and loyalty.

这里应该指的是“认同”。