You asked a few questions,
Does anyone have any idea about this? Is everything right here? Any gotchas that I need to be aware of?
It's hard to answer those, because we're getting your description of the proposed deal, and that inherently leaves some gaps.
If we take a step back, and ignore whether or not the seller is getting taken advantage of by the dealer, the only thing that matters (to you) is paying an agreed price, and receiving the vehicle and a clean, lien-free title.
Right now, we can presume that the seller's original lender has a lien on the title. That lien will be released when the remaining balance of the loan is paid off. The transactions required to do so do not require participation of a dealer - the only third party involved is the bank that financed the seller's loan. Typically, for a private party sale, the buyer and seller would agree upon a price. The buyer (you) would make payment directly to the seller's bank (this removes the chance that the seller takes the money and runs, or otherwise doesn't bother to satisfy the lien). If the sale price is more than the loan payoff amount, the buyer would remit two payments - one to the bank for the payoff amount, and one to the seller for the balance. However, in the case of this seller, it seems that they are upside down (they owe more than the car is worth). In these cases, it's typical for the seller to pay the loan down to the sales price, and then the buyer remits the full amount directly to the bank. Either way, the bank releases the lien and you happily receive a clean title.
However, the seller may not be prepared (in the financial sense) to pay the loan down enough that the balance will be equal to your agreed sales price. This is the point at which mhoran_psprep's answer becomes relevant - the seller may be trying to roll the remaining balance into a loan on their new car.
Speaking from the seller's perspective, this can be attractive, because it lets them get a new car. But, looking out for their financial health, it's almost always a bad move to take this path, since it basically means that they will instantly be upside-down on the new car (because they've borrowed more than they are buying it for). These days, few banks will be happy to do such a deal, because a buyer upside-down means that a portion of the loan balance is not protected by the collateral. As such, banks sometimes impose limits on how the transaction must play out. The bank may require that the sale is to a dealer, not a private party.
Speaking from the dealer's perspective, whether or not the seller is upside down, it's to their advantage to be involved in as much of the transaction as possible, because it gives them more variables to play with to their own benefit (which is a nice way of saying: it gives them an opportunity to take advantage of the seller). It's easier for the dealer to make the new car transaction look appealing if they have a trade-in transaction in which they can "hide" profit opportunities.
To bring this all back on track, the bold sentence above is the thing you should focus on. Make sure you understand each step of the proposed transaction, and make sure you think carefully about risk you may be taking on. Ask questions if you don't understand, and don't let the seller or the dealer pressure you in to something you're not comfortable with. If you are entering into a contract to purchase the vehicle from the dealer, make sure the terms in that contract match your expectations with respect to the negotiations you had with the seller.