"Whizzes by" means "moves quickly past". With regard to an event, it refers to the passage of time. The writer is saying that the gameplay moves quickly.
"Blur", when used literally, describes an image that is indistinct or unclear. In many cases, it refers specifically to motion blur, which is when something is unclear due to it moving quickly (for example, a photograph taken from a moving vehicle using a slow shutter speed). However, we often use the word in a broader, figurative sense to describe something that moved so quickly it was difficult to take it all in - not necessarily visually, but mentally. That is the meaning implied in your example. As it refers to gameplay and not visuals, I do not believe it is suggesting that it was visually blurred. Rather, it suggests that a lot happens and you must concentrate to keep up.
"Giddy" has a number of meanings, but I think the most apt here is "disorientating and alarming, but exciting". This word adds excitement to the description of the gameplay, and confirms that the word 'blur' is mean in a positive way.
To sum up, "gameplay whizzes by in a giddy blur" means that the gameplay moves quickly and is exciting.