I would like to know if I provide a SSIS package that contains a export to excel data flow to a third party, would they require a excel on the machine that the package runs from
No, the export to Excel functionality is a native capability for SSIS. It does require the package to execute in 32 bit mode but otherwise, it has not outside dependencies.
However, if you find the native export to functionality...lacking and implement your own export using the Interop classes, then you will need to install and license that server for Office. You will probably gain the ire of the windows administrator as this will increase the amount of patches and outage time required for this box. You'll also want to keep a very close eye on your coding to ensure you don't open yourself up to memory leaks. C# Excel automation causes Excel memory leak