Yes, this is the Blade of the Ruined King.
He also has Zhonya's Hourglass on the shelf.
Stuff like this is why people thought that the Legends of Runeterra cards are not canon, since there is alot of stuff going on in the art that seems weird.
However, we got told that the art of the card game is basically the same like the champion interactions in the game.
The pictures are more a "what if" situation. Not everything that is going on there actually happened, but it could possibly happen at some point, if the opportunity ever arises.
Just like, for example, Swain has never actually met Jinx in the lore. But he has an interaction for her in the game reading her secrets, this is what would happen if Swain would some day encounter Jinx.
So you can see this picture just as "this would be how it looks like if Ezreal might ever find the Blade of the Ruined King and Zhonya's Hourglass on his adventures".
It does not necessarily mean that these items are actually in his possession.