The tutorial uses assert from <assert.h> for real runtime errors.
Many VK_ERROR_* are "real" runtime errors, and not logical errors. Therefore it is not valid to use assert, which only executes in the debug build.
Things like OOM errors need to be caught in the release build too in order for the app to handle them graciously and not enter undefined behavior.
http://www.cplusplus.com/reference/cassert/assert/ :
Therefore, this macro is designed to capture programming errors, not user or run-time errors, since it is generally disabled after a program exits its debugging phase.