I bought an Asus 2-in-1 tablet/laptop, and it was advertised as having Office 365 for an year, and there was card with activation number. But I also got a new Asus (micro deskto) where Office was a preinstalled trial.
Most manufacturers (not just Asus) have different policies what is bundled with their products depending on the market, in the same way Volkswagen cars sold in Europe are different from same VWs in States, or South Africa, or China. So, before contacting Asus (in the country where your laptop was bought), make sure what exactly was sold on it. But even then, I doubt you will get something - if you lost your new iPhone, would Apple send you a new one just because you claim to have lost it?