How do CCGs/LCGs have an ongoing metaplot?
I decided to e-mail someone who is more familiar with the Legend of the Five Rings collectible card game and got a pretty helpful answer:
Consider for instance the Race for the Throne storyline of the L5R card game. This was a storyline where the emperor's throne was vacant with no heir and there was a sort of civil war to determine who should become emperor.
One thing that you seem to have not been aware of is that AEG publishes fiction stories online for L5R and their other games (Doomtown too). Race for the Throne had a whole collection of stories that talked about which people each clan put forth as candidates, what issues arose, who died in the conflict, and so on. This was where the majority of metaplot took place.
If the stories had something happen to a particular person, they would be reflected in a new version of their character in the next edition (or in the rare even that someone died in the fiction, they would be completely omitted from the next edition). For instance, Race for the Throne had Kitsuki Iweko as a Daimyo as a reflection of the development she gained during the Rain of Blood arc (Diamond Edition) where she was just a Samurai.
Aside from characters, the cards also tended to reflect the events of the stories as well. For Race for the Throne, these were cards such as The Throne Stands Empty, Claimants to the Throne, and Claiming the Throne. Often times, flavor text quotes attributed to certain people were in fact quotes from the fiction itself.
AEG will also base the storyline off of the results of high level tournaments, particularly the world championships. If memory serves, the 2007 World Championships were represented in-universe as the Celestial Tournament where the winning player got to have their faction crown their champion as emperor, concluding the Race to the Throne arc. The winner of the world championships was a player who played a Dragon clan deck, so the Dragon clan champion, Iweko, was crowned Empress Iweko I.
It seems the specifics about the 2007 World Championships have been taken down, but I found similar info on their website for the 2014 World Championships. For instance, there was the storyline event &quot;Something Wicked…&quot;

Even in the most prosperous of times, there are dire omens that must be heeded. In Rokugan, there is one omen that is darker than all others, one sign that causes the faithful to rush to shrines and temples and pray to their Fortunes and ancestors of choice for guidance and protection. There is one portent that is so dire that there can be no room for interpretation, but instead its presence affords certainty that there are dark and terrible things upon the horizon.
The Porcelain Mask of Fu Leng has returned.
The winner of this tournament may select any one personality affiliated with his faction. That personality will be responsible for discovering the mask’s return to Rokugan, and will be among the first to realize what disaster looms upon the horizon.

As a result of this, future stories by AEG will involve whichever person the winner of the tournament picked to be the one who found the mask.
So the ongoing metaplot happens in a couple of ways:

Fiction stories published by AEG
Cards that reflect those fiction stories
Input from players who win championships or other special events

I think that it's rare for the RPG to affect the CCG metaplot (which I think is partly why RPG players hate the CCG metaplot changes, especially since sometimes there are pretty drastic shifts in status quo). I suspect that's because the CCG is more of a moneymaker and story prizes are a really good incentive for those who care about it.