Does the item also specify that it can be used as a focus, even if your class can't normally use a wand as a focus? If not, then the easiest solution is probably to assume that you can. That would make way more sense than a cleric waving a holy symbol and gaining a bonus from the wand in her back pocket.
It doesn't state that, but why would you assume that it grants this additional benefit that it does not state that it grants.
The interpretation that seems easiest to arrive at is that it is a wand. A wand is a focus for some classes. It is not a focus for all classes. This magic item can be used by all spell casting classes, but it does not give them the new ability to use a wand as a focus. Err, so? The Cleric uses a Holy Symbol and this wand at the same time. The Holy Symbol is the spellcasting focus, the wand is a magic item that grants a bonus to hit with spells. The rules do not prevent both of these from being used at the same time.
If the item was called a toothbrush instead of a wand, I'm not sure that anyone would have come up with the idea that it could be used as a focus by all spellcasting classes.