I think it is moreso the ability to settle in one place that caused the growth of technology. The hunter-gatherers, no matter how numerous, certainly did not spend their free time building forges and experimenting with metal.
Also note that the time spent gathering food likely does not include preparing to gather food (e.g.: making weapons). Although they could spend plenty of time playing games, note that games originated to prepare children to spend time gathering food (and practice other necessary survival skills).
I must rescind this statement. As a result of these discussions, I began reading Guns, Germs, and Steel, which, in the chapter "To Farm or not to Farm," makes clear the disconnect between agriculture and sedentary living:
"Another misconception is that there is necesarrily a sharp divide between nomadic hunter-gatherers and sedentary food producers. In reality, although we frequently develop such a contrast, hunter-gathers in some productive areas, including North America's Pacific Northwest coast and possibly southeastern Australia, became sedentary but never became food producers. Other hunter-gatherers, in Palestine, costal Peru, and Japan, became sedentary first and adopted food production much later. Sedentary groups probably made up a much higher fraction 15,000 years ago, when all inhabited parts of the world (including the most productive areas) were still occupied by hunter-gatherers, than they do today, when the few remaining hunter-gathers survive only in unproductive areas where nomadism is the sole option.
Conversely, there are mobile groups of food producers. Some modern nomads of New Guinea's Lake Plains made clearings in the jungle, plant bananas and papayas, go off for a few months to live again as hunter-gatherers, return to check on their crops, weed the garden if they find the crops growing, set off again to hunt, return months later to check again, and settle down for a while to harvest and eat if their garden has not produced. Apache Indians of the southwestern United States settled down to farm in the summer at high elevations and toward the north, then withdrew to the south and to lower elevations to wander in search of wild foods, during the winter. Many herding peoples of Africa and Asia shift camp along regular seasonal routes to take advantage of predictable seasonal changes in pasturage. Thus, the shift from hunting-gathering to food production did not always coincide with a shift from nomadism to sedentary living."
Also note that the time spent gathering food likely does not include preparing to gather food (e.g.: making weapons). Although they could spend plenty of time playing games, note that games originated to prepare children to spend time gathering food (and practice other necessary survival skills).