I guess the point that it is trying to make is OK, but it oversimplifies the problem. Overpopulation is not related to merely food or space. Those are the two things this planet has enough of (we have yet to colonize the high seas! plus food replenishes itself unless one depletes the soil).
However, as the video cleverly pointed out, we're moving into more and more advanced standards of living. Where we before only required clean water, food, a place to settle and perhaps some hides to keep warm, we today need fuel, construction material etc. These resources are limited. This is not even mentioning how increasing use of these resources have devastating effects on the environment we depend on to collect food, water, living space etc. It's all about balance. Overpopulation is a complex equation of living standards, technology, climate. in addition to food and space as mentioned in the movie.
Not to mention that according to the rules of diminishing returns, the space we first use is the most suitable. As we use more and more space each square meter beomes less suitable for habitation, thus more resource consuming (problems of exposure to extreme environment, longer supply routes etc). Not to mention how our living space and the connected infrastructure increases with standard of living, and it usually grows at the expense of farmland, meaning it becomes harder to feed these people.
There might be much more, but I don't have more time. It's a nice video, but one cannot solve such huge questions in a two minute video or whatever, and should be treated as such