Because a spine, or indeed any internal skeleton is not a pre-requisite of movement. There are millions of animals that have no spine, that move perfectly well, too many to list here obviously, just put 'invertabrate' into your search engine of choice, and read on ...
Also, even though the spider has no spine, it has an exoskeleton, hence it's ability to maintain the rigidity required to walk rather than just squirm (which is the preferred method of movement of many invertibrates)