For future references for non-US authors:
I obtained my EIN from US IRS (tax institution) a couple years ago - as a non-US citizen, if your country as a tax treaty with the USA, you can actually fill an SS-4 form (https://www.irs.gov/pub/irs-pdf/fss4.pdf), head to irs.gov and search for instructions. Then, you can fax this form or send it via mail to IRS (again, irs.gov for addresses etc), and after few weeks, you should receive your EIN.
EIN can be obtained if you own a legal business in your country, there’s no need for any employees, you can be a sole proprietor. And you don’t need any type of direct connection with the USA.
I officially run EU-based business, my country has a tax treaty, and obtaining an EIN for non-US citizen wasn’t difficult - it only required patience and reading the instructions :).