The 'Edgelord' Era
To understand Shadow the Hedgehog, you have to remember 2005. This was the era of Link getting a realistic sword in Twilight Princess and Jak getting a gun in Jak II. Sega wanted Shadow to be their 'adult' alternative to Sonic, resulting in a game that feels like it was written by a middle-schooler who just discovered Hot Topic.
The Choice Mechanic
Mechanically, the game is fascinating because it actually tries to do something with player choice. Each level has a 'Hero' objective (help the humans/Sonic), a 'Dark' objective (help the invading aliens/Eggman), and a 'Neutral' objective (just get to the end). Depending on what you do, you unlock different levels and different endings. It’s a great concept that is unfortunately hampered by the fact that you have to beat the game ten times to see the true finale.
Modern Context
If your kid is coming into this after playing modern Sonic titles, they are going to be shocked by how 'loose' Shadow feels. The physics are notoriously slippery, meaning Shadow often slides right off the edge of platforms. It requires a level of patience that many modern games don't ask for. However, for a kid who loves the character, seeing Shadow ride a motorcycle and use 'Chaos Blast' is still a major draw. Just be prepared to help them through some of the more unfair platforming sections.