Does it make sense for a cake icing recipe to call for vinegar but not baking soda?
It's fine as written.

Combining vinegar with baking soda (or any acid with any base) is usually done in baking to produce gas, which can lighten the finished product. This is an icing, which is applied after the baking process; it's not set to capture air bubbles, so any effect would be largely temporary and more easily produced through beating.

The vinegar here is intended to mimic the tangy flavor of real cream cheese. The lemon juice has the same effect, but apple cider vinegar adds a different mix of acids, better matching the flavor of the real thing.