Rika and Ryo officially meet in episode 28 of Digimon Tamers but it's already implied there that they had met before on a Digimon cardgame tournament. It's Kazu that reveals this information when he accuses Rika of being in a bad mood because Ryo beat her on a tournament once and she only became the Digimon Queen after Ryo disappeared.
This is however not the first time the Card Battle Tournament was mentioned. Three random guys stop Rika on the street in episode 3 when one of them recognizes her as the Digimon Queen. He tells his friends that Rika was the one who won the Cathode Tamer Tournament but only came to the finals of (and didn't win) the Digimon Card Battle Tournament.
It's clear that the writers of Tamers had the intention of introducing Ryo's character as someone who once beat Rika on a Digimon TCG tournament. However, the two claim in episode 28 that they don't remember ever fighting against eachother.
Rika's motive for claiming she doesn't remember Ryo is understandable. She was obsessed with winning and being the best at Digimon cards for quite some time and she now had to face her biggest rival for the first time after losing the tournament to him (Ryo disappeared after that same tournament). And not only did he just save them from Megadramon, he didn't even remember her. It's clear she does know who Ryo is. Kazu, Kenta, Takato and Henry all know him as the legendary cardgame player who disappeared one day after a tournament. It's impossible for someone as engaged in Digimon TCG as Rika not to know him or remember ever fighting against him. Plus her face expressions when they first meet reveal a lot:
She's shocked when she sees him (pic#1), speechless when he grabs her hand and introduces himself to her (pic#2) and doesn't even twitch when Kazu and Kenta finally realize who he is and he confirms it (pic#3). She had to have recognized him immediately and when the shock of seeing him in the DigiWorld wore off, she wasn't ready to face her biggest rival and got super annoyed by his presence.
It's not so clear why Ryo doesn't remember battling her. Meeting Cyberdramon after that tournament, immediately going to the DigiWorld and spending 10 months there could have affected his memory of his last day in the Real World. Plus he's not obsessed with winning and probably wasn't experiencing the tournament as personally as Rika. He does seem to remember her later because he thinks about that tournament and mentions Rika when recording his message to Cyberdramon in Drama CD: Original Story, Message in the Packet:
His message confirms that he remembers battling Rika in the finals and that he disappeared to the DigiWorld after that same tournament. Henry also explains that to Terriermon in episode 29 when they meet Ryo:
It's not clear if they only fought once (Kazu does say that she was always second before Ryo disappeared) but they're definitely far more experienced and skilled in the Digimon TCG than any other player they had fought against. So much so that with one of them out of the picture, the other one didn't really have a worthy opponent anymore.
According to the three random guys on the street from episode 3 Rika won the so called Cathode Tamer Tournament. In episode 6 she remembers winning a tournament and meeting Renamon afterwards. The tournament there is called the Digital Monsters D-1 Grand Prix. It looks like she won more than one tournament after Ryo went missing and according to her interview with the tournament presenter winning the D-1 tournament was no challenge for her:
While Rika stops going to the Digimon TCG tournaments after Renamon and the other Digimon return to the DigiWorld in the last episode of Digimon Tamers, Ryo still participates and wins at them. He even travels to Tokyo from Kyushu for a tournament but then a tournament could also just be a good excuse to visit his old Tamer friends there. All of this is revealed in two Drama CDs: Original Story, Message in the Packet & Digimon Story Special ~with~ (a story that happens one day after the first Drama CD).
* We know from her message to Renamon that the reason is deeper than that and that she just feels lost without her Digimon and doesn't really know what to do with her life now that she stopped fighting:
* Ryo seems to enjoy fighting in (card)games and is considering finding a new game to play. It is implied a bit that he outgrew the Digimon TCG - not only can he not find a worthy opponent anymore, he's also older than all of them and doesn't feel like he belongs there anymore. (This often happened in my YGO TCG years when older players changed to Magic the Gathering because people were older there and the game felt more serious. 8) )
Rika on the other hand doesn't feel like fighting anymore but in the end seems to find her purpose in competing anyway, when she leaves her modelling career for FMX, freestyle motocross.