Day by day they bring out new cards, I wonder if someday the royalties will end and if so when approximately?
It will end
Each card has its own copyright. Using the united-states as the basis, because most countries mimic them, the copyright for a published work with a known author ends approximately 70 years after the death of the author or 95 years from publication for company-owned copyrights.
The Yu-Gi-Oh manga was first published in 1996 and its author died in 2022, so the underlying manga will enter the Public Domain in 2093.
The card game consists of three elements: the cards themselves, the artwork on them and the rules. The rules aren't copyrighted. The artwork's copyright is tied to the artists making it, if it is licensed art, or the company, when it is work-for-hire, so might or might lapse at two points: 70 years after the artist's death or together with the card. The card's copyright in the compilation lapses 95 years after the publication. The first set of Yu-Gi-Oh cards was published in 1999, so the copyright will lapse at the earliest 2095 on the first card set. But only that first card set. Other card sets will enter Public Domain when their 95 years are up.
Japanese copyright expires 70 years after the death of the author.
Kazuki Takahashi sadly passed in 2022. Copyright in everything he authored will expire 1 January 2093. Anything authored by others will have a different expiry.