Short answers, pulled from the story.
The Legend of Zelda: Ocarina of Time was released on the 21st of November 1998. This title remains Metacritic's highest-scoring game of all time and set a new standard for action-adventure games.
Pokémon was the best-selling home video game worldwide in 1998. The game sold over 4 million units in the United States alone and generated $70 million in revenue.
Sega launched the Dreamcast console in Japan on the 27th of November 1998. This machine was the first console of the sixth generation and introduced features like the VMU memory card and online play.
Tekken 3 was the highest-grossing arcade game in Japan in 1998. The fighting game was released on the 26th of March 1998 and became a staple of arcade culture.
The Game Boy Color was released on the 21st of October 1998. This handheld system introduced color to the market and allowed developers to create games that utilized the new color palette.