Licensing standalone instance of SSIS Basic background:  I have an application on an app server (no MSSQL installed) that I want to allow to call an SSIS package.

One Solution:  One option seems to be that we can install just SSIS on the app server without needing to install SQL Server itself.  The app would be able to run a package while referencing the DB itself on a separate server.

Question:  Would this require licensing SQL Server on the app server, even though the core engine is not part of the installation?
Yes. Now my disclaimer is I'm not your licensing rep or Microsoft so you should check with them on questions.

But the verbiage in the various license guides is typically "A Server running SQL Server - or any of its core components (SSRS, SSAS, SSIS)". 

So if you are using SSIS on a server standalone, by the licensing guidelines you are running one of the core components on another server and that should be licensed separately from any other machine running a core component.

Depending on the load of your SSIS server, I have typically found that in many installations, just running the SSIS server on an already licensed machine - be it your warehouse server or a staging server or even your main production server works.

When you get into complex SSIS workloads with lots of moving parts and pieces and high overhead, you may start considering a separate processing server that perhaps also contains the DB instance for your SSIS logging and reporting type of environment. I'd say that I have to consider that sort of separation for performance rarely lately, though I have in the past. 

Microsoft publishes several detailed and overview license guides. This one here is an example for SQL Server 2012.