Learn French: Cet acteur a le même style que son sosie. - This actor has the same style as his lookalike.

Because it has to agree with the noun it describes. Style is a masculine singular noun in French, so we use the masculine singular form le même. If the noun were feminine, like couleur (color), it would be la même couleur que.

Does que mean "as" in this sentence?

Yes! When you want to express "the same [noun] as" in French, the "as" is always translated to que. While que often means "that" or "what" in other contexts, in comparisons like le même... que, it is the required word to connect the two things being compared.

Why is it Cet acteur and not Ce acteur?

Acteur is a masculine singular noun, so the standard word for "this" or "that" would be ce. However, because acteur starts with a vowel, ce changes to cet to make it easier to pronounce and avoid a clunky clash of vowel sounds.

What exactly is a sosie?

A sosie is a lookalike, a body double, or a doppelganger. It is always a masculine noun (un sosie). This means you must use the masculine possessive son before it (son sosie), even if the lookalike in question happens to be a woman!