Games does not just mean the type of game played between two people moving rocks around. Racing is a game and sport, human, animal or combination. It is also linked to gambling.
The modern Olympics is a poor version of the classic era Celtic Lugnassad(sp?) which did not only have atheletic activities but also poetry and strategic game components.
Can you explain a little more? Your wording is really confusing me. I can see Games pointing towards Athletics (maybe as an OR prerequisite with Military Training, and then have it be required for Combat Sports).