Silicon was discovered in 1824, long before Mendeleev published his periodic table in 1869. The properties of silicon were already known and studied by chemists.
Mendeleev's genius was in organizing the elements based on their known properties and predicting the existence and properties of undiscovered elements. He left gaps in his table for elements that had not yet been discovered, and he was able to accurately predict the properties of these elements based on their position in the table.
However, silicon was already a known element. Mendeleev used silicon's known properties to help him understand the relationships between elements and formulate his periodic law.
He didn't predict silicon's properties; he used them as a foundation to build his groundbreaking periodic table.