Learn Finnish: Pelihallissa on uusi flipperi, jota voi pelata yhdellä poletilla.

In this context, it primarily represents the price of a single game, aligning with the adessive of price and transaction. However, because a token is also the physical object inserted into the machine, it overlaps perfectly with the adessive of instrument (meaning 'by means of'). Both uses require the -lla/-llä ending.

Why is the relative pronoun joka in the partitive form jota?

The relative pronoun takes its case from its grammatical role in the relative clause. Here, it is the object of the verb pelata (to play). Because playing a game is treated as an ongoing action, pelata requires its object to be in the partitive case.

Why is there no subject pronoun before voi pelata?

This uses the zero-person construction. By using a third-person singular verb (voi) without an explicit subject, the sentence implies a general 'one can play' or 'you can play' referring to anyone in general.

Could I change the beginning to Uusi flipperi on pelihallissa?

You could, but it changes the nuance. The original sentence starts with the location (Pelihallissa) to introduce the existence of something new ('There is a new pinball machine...'). Starting with the subject would translate to 'The new pinball machine is in the arcade', implying the listener already knows which machine you are talking about.