This is a horrible situation, because the seller probably feels she shouldn't need to accept PayPal, while your daughter feels she should be able to pay by PayPal.
As sympathetic as I am to the seller, the cold hard fact is that unless one has a PayPal account on eBay, one is in a very equivocal position as a seller - since eBay flatly state that all sellers must accept payment by PayPal (for most types of transactions). That I think this is unfair is beside the point... It's hard to think the seller was unaware of the requirement to accept PayPal payments.
Is this a new or inexperienced seller?
At any rate, this is the situation: your daughter has paid money to an email address which she assumed to be a PayPal account. That doesn't mean the email address does have a PayPal account attached to it: that's simply the default email address which eBay treats as if it were a PayPal account in lieu of another email address being entered as the PayPal account.
The money is thus unclaimed, hovering in The Great Wastelands.
The seller can set up the PayPal account and claim the payment, and would in fact be well advised to do so because failure to accept payment by PayPal leaves sellers open to reports as a non-performing seller. That can and will lead to the seller's eBay account being sanctioned, leaving her unable to sell (and possibly unable to buy).
But if your seller flatly refuses to get a PayPal account, your daughter can't force her to do so. (Neither can eBay. They can sanction her eBay account but they cannot make her have a PayPal account.)
How trustworthy does the seller appear? What's her feedback like? Will your daughter prefer to cancel the transaction without reporting the seller? Will your daughter prefer to report the seller? Would she prefer to buy the game from a different seller?
The best option will be dependent on what your daughter wants to achieve. If the game is better value from this seller than from others sellers, and if the seller's feedback as a seller indicates she's trustworthy, that's one option - for your daughter to cancel the unclaimed payment (by going to her PayPal account) and then paying again via bank transfer. However, if your daughter doesn't feel trust in the seller, she may decide that's not advisable, particularly if it's a large amount of money.
At any rate, your daughter is probably best off cancelling the PayPal payment because it doesn't seem as though the seller is going to open up a PayPal account. Then it's up to your daughter about whether or not she wants to report the seller... whether or not she wants to pay by a different method... and so on.