Wow, that was quick. I thought it take a bit more time, oh well. Sorry Eaglegun, but Karifean is correct. So we now have an open floor. Here's my riddle explanation:

In circles I run,
One card I hold may be won.
He is the underclass man jogger in the First floor Hall of Balamb Garden. He wears a yellow shirt if I'm not mistaken, but he is always running in a circle.

He is a Triple Triad card player, but he only has one card of interest: the Mini-Mog GF card. I would like to know where the name Mogry Kid for the Mini-Mog card came from, Karifean.

I reside where seeds are planted,
There is one which grew to Command fellow seeds,
But I am not a seed.
You've seen me many times.
A garden is where seeds are planted. So a Garden is where SeeDs are planted. So your thought of seeds equaling SeeDs is correct.

Squall is the SeeD who became the Commander of Balamb Garden, and now commands his fellow SeeDs.

This underclassman is not a SeeD at all, as far as we know that is.

That last line refers to the answer.

There are two places on this island,
Which share the same name,
It is also where all of the seeds started.
The Balamb Garden and the Balamb town are both on the Balamb island.

My card? Why, it is a knight,
But unavailable through the average means.
Yes, knight does mean GF in this case. And yes, this GF is only available through the Chocobo World side-game. The GF in question is the Mini-Mog.

Which card do I hold?
And who am I?
He holds the Mini-Mog card.
He is the underclassman jogger found in Balamb Garden.

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Could anyone give me the Japanese script for the Mini-Mog card?