Learn Finnish: Shakki on yhtä strateginen kuin tämä peli.

In Finnish, "as [adjective] as" is expressed using the structure yhtä [adjective] kuin. The word yhtä is literally the partitive form of yksi (one), but here it functions as an adverb meaning "equally."

Why isn't the adjective strateginen in the partitive case after yhtä?

Because yhtä is acting as an adverb here, it does not force the word following it into the partitive case. The adjective strateginen is describing the subject shakki, which is in the basic nominative case, so the adjective simply matches that case.

I usually see kuin translated as "than" in comparisons. Why does it mean "as" here?

The word kuin handles both depending on the context! When paired with an adjective in the comparative form (like strategisempi), it means "than." But when paired with yhtä and a basic adjective, it completes the "as... as" structure.

Could we include the verb on at the end to explicitly say "as this game is"?

While adding on at the end (...kuin tämä peli on) is grammatically possible, it sounds clunky to a Finnish speaker. It is much more natural to leave the second verb out entirely.