No it doesn't. Verse 3 of chapter two clearly says that it was the 7th day, and God was resting. Then the rest of the events in Genesis two occur after that (presumably day 8+, since God rested on the 7th). The events in Chapter two could occur in any time after the 7th day of creation; they are not limited to a single day and thus the entire argument presented at the posted site is fundamentally flawed.
Those that suggest that the universe couldn't be created in 7 days just don't understand the nature of time; the passage of time, and it's measurement, is dependent upon the frame of reference of the observer.