Learn Spanish (Latin America): Para el presentador, esto no es más que un simple juego. - For the host, this is nothing more than a simple game.

No es más que is a restrictive negation meaning "is nothing more than" or "is nothing but." It emphasizes that the thing being discussed is only that and nothing greater. You could absolutely say esto solo es un simple juego (this is only a simple game), but no es más que adds a stronger, slightly more dramatic sense of limitation or dismissal.

Could I use sino in this sentence to mean the same thing?

You could, but the structure would change slightly. Sino introduces a corrective contrast (not X, but rather Y). To get the "nothing but" meaning here, you would usually pair it with an absolute negative like nada, making it: esto no es nada sino un simple juego. However, no es más que is the much more natural and common way to express "nothing more than" in everyday Spanish.

Why is simple placed before juego instead of after it?

When simple goes before the noun, its meaning shifts to "mere" or "just a" (a mere game). If you place it after the noun (un juego simple), it describes a game that is uncomplicated or easy to play. Placing it first perfectly reinforces the dismissive tone of no es más que.

Why use the neuter pronoun esto if juego is a masculine noun?