How I envision it:

Location
I don't think there needs to be a specific area for casual games. In the menu, just add a challenge option and go about it like you would trade. You get challenge, you accept, the Triple Triad Menu pops up for selecting cards and the board in the middle. The only limiting factor to this is that you should only be able to play in cities, camps and hamlets.

Whom you may challenge
Any player who has Triple Triad Status active. When you or your opponent accept the challenge, you both go into the "synth" kneeling position. Your deck could have an average level based on the tiers and strength of the cards you have, so Jimmy Thenoob doesn't get splattered by a Primal hand.

Rules of the Game
Rules and How-to-Play

Acquiring Cards
-Random chance to drop off monsters.
-'Card' ability to convert a weakened monster into a card. EXP and drops are forfeited. Cannot be used on Notorious Monsters.
-Crafted. (Ifrit's Horn + Blank Card = Ifrit's Card)
-Quest and Leve rewards.

Card Uses
-Used in games of Triple Triad
-Collection and Trade
-Refined for items (Bomb Card = Stack of Bomb Ash)
-Converted to Materia (Win X number of games while using a card, where X is the level of the card x5)

Crafters and Materia
Refining a card, like in FFVIII, would allow crafters to also make use of the system. Refining a card can have various yields and all dependent on the card's level.

For example, Refining a card for a Marmot (Level 1) may yield a few marmot pelts. Refining an Ifrit card (Level 8) would yield an "Infernal Catalyst x3" for use with an Infernal Materia.

Infernal Materia you ask?

Card Materia
Only level 8 and higher cards may be converted to Materia. When deciding how you want to apply a powerful card to an item, you have two choices. Refine it for the Catalyst or Spiritbind it for the Materia. Ultimately, you will have to acquire a second copy of the card if you wish to get both or buy the catalyst.

The materia would be unique. "Infernal Materia" would require the "Infernal Catalyst" to be set. The materia could be extremely potent.

Infernal Materia: STR+50, DEX+50, Fire Resistance +50, Adds Fire Elemental Damage. Placed in a GLD/MRD/LNC/ARC/PGL arm.
Tidal Materia: MND+50, INT+50, Water Resistance +50, Adds Water Elemental Damage. Placed in a CNJ/THM arm.
Earthen Materia: DEF+50, VIT+50, Earth Resistance +50, Adds Earth Elemental Damage. Placed in a Shield or Body armor.

Copies of Cards
I would recommend cards leveled 1-7 be allowed to have 3 copies. Card levels 8-10 would be exclusive one copies.

But wait, there's more!
Why limit the Catalyst to just materia? Let's put some power in the crafters hands and help the DoW with that pesky Ifrit weapon. Bring an Infernal Catalyst and an Ifrit's Horn to a crafter and watch them work their magic! One recipe with these two items would allow the crafter to make the appropriate Ifrit weapon.

I love this card game with a passion. If SE put it into XIV, I'd die happy. Hell, I'd buy it if it was a stand alone game. But I'd do the same for Blitzball too. xD