The source you cite from the WHO is fairly authoritative, so the best I can do is point to other sources that are consistent with that source.
"Approximately 469,000 people age 65 or older will develop Alzheimer’s disease in the United States in 2014." (https://www.alz.org/downloads/Facts_Figures_2014.pdf at p.19)
That is approximately 1300 / day.
The United States population is approximately 1/20 of the world population – naively multiplying gives an estimated world-wide incidence Alzheimer's of approximately 26000 / day.
Thus the estimate of a diagnosis every 4 seconds is consistent with the incidence of Alzheimer's disease in the United States.
The World Alzheimer Report from 2009 (http://www.alz.co.uk/research/world-report-2009) estimated a slightly lower incidence:
With a new case of dementia in the world every seven seconds there is no time to lose.
with 4.6 million new cases annually
That number is supported by (Ferri, Cleusa P., et al. "Global prevalence of dementia: a Delphi consensus study." The Lancet 366.9503 (2006): 2112-2117.):
Applying the DISMOD estimated incidence rates, we estimate 4.6 million new cases of dementia every year (about one new case every 7 s).