I recently watched a Jeremy Rifkin video in which he stated that a 1°C increase in temperature resulted in a 7% increase in atmospheric water.
Seven percent seems like a pretty big number. If true, why wouldn't this cause the sea-level to decrease?
No, 7% is somewhat too high.
According to Recent Climatology, Variability, and Trends in Global Surface Humidity Journal of Climate, (2006) volume 19, pages 3589-3606:
The observed dq/dT is about 0.58, 0.38, and 0.77 g kg-1 °C-1(r2 = 0.81, 0.77, and 0.76) for annual q and T for the globe, global land, and ocean, respectively. In percentage terms, they are about 4.9%, 4.3%, and 5.7% change in q per 1°C warming, which are close to those (∼5.4%, 5.1%, and 5.5% per 1°C, respectively) suggested by the Clausius–Clapeyron equation or its empirical version [Eq. (3)] for saturation specific humidity (computed locally and then area averaged). 1
where "q" is specific humidity, "T" is temperature, and "dq/dT" is the rate of change of specific humidity with respect to temperature.
and where footnote 1 is:
The Clausius–Clapeyron equation locally gives 6.2%–6.4% change per 1°C in surface saturation specific humidity (qs) for air temperature within 15°–20°C. For regional averages, however, this percentage is lower because the area-averaged mean qs is higher than that calculated using the Clausius–Clapeyron equation and area-averaged mean air temperature and pressure.
So, in conclusion, the correct value is 4.9%.
globally water vapour increases by 7% for every degree centigrade of warming
Scientific America agrees, and references the claim to Peter Stott, from the Met Office.
And for every 1-degree C (1.8 degrees Fahrenheit) rise in temperature, the amount of moisture that the atmosphere can contain rises by 7 percent
In response to your secondary question of "If true, why wouldn't this cause the sea-level to decrease?" - Climate Central says that a 1.5C rise could cause a 2.9m sea level rise. This is significantly more than the reduction caused by increased humidity. So the 7% increase would cause the sea level to reduce (slightly), but the rise from other factors (expansion of water, and melting land ice caps) would quickly outstrip it.
As a sidebar, I do not know of Jeremy Rifkin, but the little I watched of the video you linked did not impress me. I would not take what he says as gospel (for example, just after he makes the 7% claim, he seems to start cherry picking different disasters that occured recently - this is not very scientific).