An SSIS package can only be run on an SSIS Server of the appropriate Edition Level. Although you can author a package using BIDS on a machine with only the SQL Client tools installed, it will not run from the command line on that machine without SSIS installed. There is no included remote execution functionality for telling a package to run on the SSIS server from a client machine (other than the SQL Job agent, arguably). Running the package on a machine without the correct edition of SSIS installed gives a vague error message about insufficient product level.
An SSIS package can be executed from within an application using the DTExec command line or through the SSIS object model, but you must be on an SSIS server. So, if you intend to distribute an application that runs SSIS packages locally on a workstation, be prepared to purchase and install a SQL Server license on every client machine.
It is pretty easy to build a web service that will run an SSIS package on the server. It can then be called from a client machine and only require a SQL CAL rather than a full SSIS install on each machine.