Americans don't use the word in that way. Even the Brits no longer use the word in that way. In the entire world, the only ones still using "Varsity" to mean "University" is the Straits Times. Outdated and irritating to read.
Another similarly irritating example from Straits Times, is the use of the word "treble" instead of "triple".
While both are technically acceptable to mean the same thing, "triple" is by far the more commonly used word these days, and Straits Times just sounds annoying in always using "treble" instead of "triple".
Additionally so when the word "treble" is most often used these days in the context of music, ie. "bass vs treble".
There are quite a number of other examples from the Straits Times, but the 2 examples above are irritating enough.
On a related note, though not about the Straits Times, is the dual use of the word "concerning".
Eg. Concerning this concerning matter = Regarding this worrying matter.
When the exact same word is used to mean 2 totally different things, it becomes irritating syntax. But can't blame the Straits Times for this one.