Character models and textures clearly show their age, but nothing is offensively bad. That being said, some of the level design and the town itself still hold up pretty well. This is not a full remake in the vein of the recent Destroy All Humans release (a game that shares many aspects of tone and theme) so you are getting a game that is over fifteen years old now. Graphically Stubbs is understandably dated.
From here you must shamble ever onwards until you discover the real reasons behind your death and return from the grave. Effectively all you know at the start of the game is that you are a zombie and that you are in a retro-futuristic town called Punchbowl that benefits from revolutionary new power sources. The initial tutorial is functional (although the ironic achievement for completing it is an example of the annoying trend for developers to think that saying a game action is boring excuses its inclusion) and abilities are gradually introduced at a good rate throughout the game. There is little in the way of explanation as to why you are playing as a zombie and your only real motivation an unending desire for sweet, sweet brains. For new players coming to Stubbs without the benefit of nostalgia, the beginning of the game is refreshingly obscure.