There's a lot of research about how people understand numbers. In general, you can group these questions under the concept of numeracy (that is, the human ability to define and apply simple numerical concepts; it's essentially literacy for numbers).
Language has a profound effect on numeracy. For example, research shows that there are some cultures whose counting is limited to "one, two, three, many". (Those of you who have read some of the Discworld series by Terry Pratchett will recognize this as how trolls count.) These cultures have a difficult time understanding the difference between, say, 20 and 30, let alone numbers as large as the counters illustrated above. If you'd really like to learn more about this topic, "Core systems of number" by Lisa Feigenson et al is a fascinating discussion.
Science and math teachers can come up with many examples of how they teach children to understand large numbers. A web search for "understanding large numbers" will reveal many different resources for children across grade levels for understanding this concept. There is also research here about how understanding large numbers impacts how students understand key scientific concepts; for example, Students' Understanding of Large Numbers as a Key Factor in Their Understanding of Geologic Time addresses this for one example of large numbers. Innumeracy: Mathematical Illiteracy and Its Consequences by John Allen Paulos is an excellent overview of much of the research regarding numeracy, and how innumeracy impacts individuals and society.
Much of the research about numeracy makes the point that humans are generally good at understanding the difference between relatively small numbers, and that we're also generally good at creating and understanding approximations of numerical magnitude. To answer the question about whether these counters are usable, I think we have to figure out whether the exact count is meaningful, or whether a simple understanding of the magnitude of a number (or, perhaps, the understanding of the difference in magnitude between two large numbers) is meaningful. In the YouTube case, I think that glancing at that number and thinking, "wow, that's a lot of views" is sufficiently usable. As a user, I'm unlikely to care whether the video has been viewed 1,121,289 or 1,122,289 times, because that difference of 1000 views isn't important. The magnitude of number of views is the important piece of information that's being conveyed.