The Dominaria printing of Mox Amber has a person's shadow on the right side of the art. It looks like the person has either a helmet or horns. They are the wrong shape for Nicol Bolas. Is this the shadow a known character from Magic?
I could not find any reference to the in-universe backstory of the art. If the shadows really do represent named characters, it is not clear who they are.
Higher resolution image of Mox Amber. It's not even clear to me that a character really is casting the shadow.
Regardless, the best I could find about the piece's backstory was the blog of Steven Belledin, the card's artist, which has a post on Mox Amber and the process of its creation. Apparently, Steve Belledin had rather large freedom in designing the art of Mox Amber. He only mentions 2 stipulations by the WotC art direction, one of which was later dropped:
What Wizards asked for initially was a little confounding to me, but it subsequently was simplified a bit. To start, they wanted a silver necklace with the amber being the necklace's charm. The necklace would be cradled in someone's hands. However, there were two specific stipulations: 1) the piece should not feel like it was part of Volkan Baga's cycle of mox paintings that also include the various moxes cradled in hands; 2) there should be no recognizable things floating in the amber (I assume to avoid any reference to Jurassic Park).
Obviously, the "cradling hands" part was later dropped, after some preliminary sketches. Further considering that
I spent a lot of time trying to hash something out in my sketchbook, but in the end I found it easier to take a piece of my wife's jewelry and arrange it in different ways on the back of her splayed leather jacket
it seems unlikely that the art of Mox Amber is deeply tied to the game's lore.
Just for good measure, I left a comment in the comments section asking about the shadows, but I don't expect an affirmative answer.