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According to this video only 10% of the fish biomass that was in the ocean during the pre-industrial era is left, due to overfishing.

This claim seems to be based on a study by Myers and Worm which has been published 2003 in Nature.

This seemed overblown to me. And at least one source (admittedly a somewhat activist looking website on the other end of the spectrum) claims, that there have been big problems with the study. It cites three further papers (Walters (2003), Hampton et al. (2005), and Polacheck (2006)), which I have not looked into.

Is the 90% figure true, completely overblown or lies the truth somewhere in between?

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    Most fish have a short lifespan, but the Japanese Koi has been known to live up to 228 years, so it's possible 10% of the fish alive before the Industrial Revolution, if they are Koi, are still alive... :)
    – Flimzy
    Nov 25, 2013 at 13:15
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    Well, as an example, some say the North Atlantic Cod Stock biomass is now at 10% of its pre-1992 levels. I do not know how it compares to other stocks.
    – Brian M. Hunt
    Nov 25, 2013 at 15:24
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    My skeptic alarm was going ballistic during that video. The claims were half-truths and misrepresentations of the reality of over-fishing. If you want a video on this topic, what these from Minute Earth: youtube.com/watch?v=u9YOVuEQugE youtube.com/watch?v=pp7BZjJkc_8
    – Tim Scanlon
    Nov 27, 2013 at 0:32

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It is difficult to get an accurate value of fish biomass:

Conclusive stock assessments of fish populations can be difficult to obtain. Ocean fisheries are particularly difficult to assess, as populations can be widely distributed, are frequently migratory, and can be affected by environmental conditions such as water temperature and current patterns.

Also there is the human element to assessment. A problem that ecologists have identified regarding measuring fishery populations is shifting base lines. When ecologists study declining populations, there is a tendency to judge the population based on the life-time memory of those who study the organisms. Older ecologists will remember the abundance of their youth and will assume this represents a normal population level. When a population has been declining over a period of decades or even centuries, this creates a skewed vision of the organisms' functioning role and carrying capacity within an ecosystem. To obtain a better understanding of declining fisheries, scientists have begun to look to history for answers regarding how much exploitation aquatic species have been subjected to over time, and what undepleted population levels may really have been. Some scientists and historians have suggested that it is necessary to look back at least as far as the Middle Ages to better understand what unexploited aquatic resources may have looked like.

Source: Carolyn Scearce. European Fisheries History: Pre-industrial Origins of Overfishing. 2009

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