So the best source for payroll in Washington is the Employment Security Department. Employers have to file quarterly reports divulging their payroll for the purpose of calculating their unemployment insurance taxes.
We're helped here by the fact that Microsoft has chosen to classify itself under NAICS code 511210 (Software publishers). This distinguishes it from Amazon and Google, which use other codes.
In Q2 2013, the most recent quarter for which they released data, all 511210 employers had a total of $1,810,714,302
for quarterly wages. So that would work out to about $7.2B per year.