Racheter means not only to buy for a second time, but also to buy something that someone else bought in a first instance, and not from a shop, a reseller or a flea market seller.

Ex:

J’ai beaucoup aimé ce vin. J’ai bu toutes mes bouteilles, alors j’en ai racheté (I have bought the same item a 2nd time)

Mon voisin n’utilisait plus sa voiture. Alors je la lui ai rachetée (=I have bought it in 2nd hand, from the person who bought it in the 1st place).

If this persons says he wants to racheter a restaurant, he means he plans to buy an existing restaurant to its current owner.

Note it would be awkward to say that anyone has "acheté" the restaurant in first instance anyway: when someone decides to start a restaurant as a business from scratch, they may buy or rent a house or a building for it, hire some staff, buy the furniture, the equipment, etc. – but at least in French you cannot consider that the founder/entrepreneur/chef has acheté a restaurant by then, he has rather fondé/lancé/démarré un restaurant. So the transaction by which someone takes over a restaurant would indeed be racheter, because it means buying something to the current owner and not from some sort of reseller.

More generally, if the transaction means a takeover of a business or a company, the verb is indeed always racheter:

Disney a racheté Lucasfilm

L’état a racheté Air France

Mon associé est intéressé par un rachat de mes parts