Hard drives know the outer tracks (the "front" of a partition) are faster, and will try to put data there first. If your game is towards the inner tracks, you will need to find files which are filling up the outer tracks, move them and the game to another drive, then copy the game back first. The HDD should then try to place it in the outer tracks vacated by your other files.
That said, the speed difference is not that big - roughly 1.5x-2x best-case. It's mostly sequential reads of large files which are sped up from being on the outermost tracks, whereas the read time for most games is taken up by small files. A SSD will provide anywhere from about 5x to 300x times the speed increase (with the 300x being for small files). So it...