Even that is not necessarily so, often when you purchase software you are only purcasing a licence to use that software and if you study the small print carefully you may find you are not permitted to resell that licence. In that case you are not the owner of the actual sofrtware.
Umm, actually that's incorrect. It is obviously within your property rights to resell, trade or give away anything you purchase - the only exceptions that come to mind as far as software is concerned are pieces of software you acquire with special pricing and licensing (e.g. student pricing: you obviously can't buy an academic version of Mathematica and then resell it for five times as much on ebay) and software received with special contractual obligations (for instance an NDA or something else).
But these are special cases, where you will have signed a contract before even getting your hands on the software. In the normal case, you can go to any electronics store and purchase a software package or game over the counter and you can sell it to anyone you please. The software manufacturer can put anything they want into their EULA - it doesn't make it legal or legally binding. An EULA can only become binding if you open and use the software, and even then certain parts of an EULA may not apply to you, depending on where you live or may be invalid altogether, because they are contradictory to the law (not uncommon).