Actually that particular Starbucks (and most Starbucks in Tokyo) opens at 7am ish on Weekdays only. On weekend and holidays that store opens at 9am. You don't get a lot of commuters/workers on a weekend as you would on a weekday.

But as mentioned, commuting times, mode of transport and work times have a lot to do with it. Many folks are traveling in from the suburbs, a trip that takes 1-3 or more hours, typically leaving home around 6 or 7, arriving into at 8-10 am, makes sense for stores to be opening around those times for the large influx of commuters and peak business.