The game will run from whatever location is was installed to.
If the files are on the HDD then it will run on the HDD if it is on the SSD then it will run on the SSD.
It has to access the files from where ever they were installed and that determines things like loading times based on the hard drives read and write speeds.
You cannot tell the program to run on the solid state drive because the files are not on the solid state drive.
The only performance hit you should suffer are loading times.
The only other benefit from an SSD for gaming is if you record at very high resolution and frame rate with RAW data which requires a very fast dedicated Raid 0 setup or solid state drive to write the large files to.
