An SVN server will do some types of merges itself, particularly when the changes are to different files as in your case. Since SVN represents branches and tags as different parts of a single tree and a single repository can contain multiple, unrelated projects this is necessary.
But git will never do a merge on the server. And since a commit represents the entire tree, your situation is a merge even though no single file was modified by both sides that need to be merged.
Even though changes being restricted to different files guarantees that there won't be any textual conflicts between them, there can still be semantic conflicts. Imagine if you're working on a change to a library function which requires all callers to be modified, and before you push that change out another developer adds a new file which contains a new call to that function. If that new file is the only change the other developer made, SVN would allow you to commit your changes and handle the merge on the server even though that will cause the code to be broken. By requiring that all merges happen under developer control, git at least gives the opportunity for this type of conflict to be caught; even though in many cases a developer may just do an automatic merge and push the results without any checking.