That Wikipedia article and several visible results from Google searches on this topic appear to draw their information from a Rensselaer Polytechnic Institute press release, http://news.rpi.edu/luwakkey/3074.
Going back to the source, it does indeed indicate that exposure to self-luminous displays for less than two hours still has an effect.
The actual melatonin suppression values after 60 minutes were very similar to those estimated using a predictive model of human circadian phototransduction for one-hour light exposures.
The reason the author provided for why this is problematic for sleep:
Melatonin is a hormone produced by the pineal gland at night and under conditions of darkness in both diurnal and nocturnal species. It is a “timing messenger,” signaling nighttime information throughout the body. Exposure to light at night, especially short-wavelength light, can slow or even cease nocturnal melatonin production. Suppression of melatonin by light at night resulting in circadian disruption has been implicated in sleep disturbances...
You rightly point out that the referenced study from RPI is quite small (limiting the statistical significance that can be inferred), however there have been many studies on the effects of artificial light over the years.
For example, an earlier report with contributions from people at the University of Connecticut, Bassett Research Institute, Jefferson Medical College, Thomas Jefferson University, the Danish Cancer Society, Harvard Medical School, the University of Virginia, the US National Institute of Environmental Health Sciences, and others in addition to Rensselaer had this to say:
Humans have evolved over millions of years and adapted to a solar day of approximately 12 hr of light and 12 hr of dark, latitude and season permitting. Our ability to artificially light the night began about 250,000 years ... However, only in the last 120 years has environmental illumination begun to change on a pervasive scale for the masses of people through the introduction of electric lighting. ... It has become apparent, however, that although of obvious benefit, it may not be completely innocuous. Light, including artificial light, can be potent in regulating human physiology and behavior and can therefore alter human physiology when inappropriately timed. One example of potential light-induced disruption is the effect of light on circadian organization, including the production of several hormone rhythms. Changes in light–dark exposure shift the timing of the circadian system such that internal rhythms can become desynchronized from both the external environment and internally with each other, impairing our ability to sleep and wake at the appropriate times and compromising metabolic processes. Light can also have direct acute effects on neuroendocrine systems, for example, in suppressing melatonin synthesis or elevating cortisol production that may have untoward long-term consequences.
In short, the accuracy of the claimed 0.18% per minute suppression of melatonin does not appear to be independently verified. Notwithstanding, the vast majority of scientific literature on this does agree that artificial light at night can adversely affect sleep.
