The question that determines your legal rights is whether compatibility with Windows 10 once it is released is a term of your contract with PC World. Your contractual remedies lie solely against PC World as you have no contract with Asus.
Unless PC World expressly promised Windows 10 compatibility (for example by including "Free Windows 10 upgrade" in any contractual paperwork), the relevant legislation is
section 14(3) of the Sale of Goods Act 1979 as you entered into the contract before the new Consumer Rights Act 2015 came into effect. Unless you disclosed at or before the point of sale (and therefore contractual formation) to PC World that you required Windows 10 compatibility, or your words or actions towards PC World implied you required this compatibility, I am fairly certain that you do not have a winnable case under contract law.
It would be for you to show that you had more likely than not made the required statement or carried out the required acts, as you seek to rely on them.
Promises on the manufacturer's web site about future compatibility do not form part of the contract between you and PC World. Advertisements, including web pages, have limited enforceability under contract law (as they are often an invitation to treat and no more), so your claim would have been doubtful even if you were relying on a PC World advertisement.
I would be surprised if PC World did not do its utmost to negate any reliance on manufacturer's claims of future upgradability, as these often turn out to be economical with the truth. If you want compatibility with a particular operating system, it is best to wait until that operating system is available, making that compatibility an express term of sale.
If you want to rely on manufacturer promises, it is best buy directly from the manufacturer (e.g. buying from Dell direct). Of course, buying directly from Dell is not entirely straightforward as, unless things have changed since I last dealt with them, you form a contract with an Irish company which I would expect to be subject to Irish law.