Are the rules different for qualified versus non-qualified dividends? Assuming no DTAA exists between the US and the country of residence.
While the other answer stated that "[qualified and non-qualified NEC dividend] is taxed at a flat rate, 30% if no treaty rate applies", Portfolio Interest (as defined in 26 USC § 871(h)(2)) and Qualified Interest Income (as defined in 26 USC § 871(k)(1)) are withheld at flat rate, but not taxed (i.e. refundable through 1040NR).
In the case of securities, certain ETF holding treasury or corporate debt fall into Portfolio Interest or Qualified Interest Income (Not to be confused with Qualified Dividend). The 1042-S issued by the broker would tell you how much is withheld, how much is taxed, and the exemption reason, and you may have to obtain refund through 1040NR on your own.
To determine whether your broker has correctly classified the ETFs as Qualified Interest Income, the issuers of the ETF publishes the percentage of dividend that is QII on an annual basis. For example: https://www.ishares.com/us/literature/tax-information/qualified-interest-income-qii-percentages-2019.pdf
Like all US taxation of NRAs, it depends substantially on whether the income is considered 'effectively connected' with a US 'trade or business', which in turn can depend on numerous, sometimes complicated factors you don't specify. See pub 519 (also available in PDF at https://www.irs.gov/publications).
If dividend income is effectively connected, you report it in the main section (p1/2) of 1040nr on line 10a,b and compute tax on effectively connected income in mostly the same way as 'residents' (1040 filers) do, using either Schedule D worksheet or Qualified Dividends and Capital Gains Worksheet either of which does apply lower rates (depending on bracket) to qualified dividends (and also to long-term capital gains, if those are US taxed at all).
If dividend income is not effectively connected (but is US source), you report it in schedule NEC (p4) of 1040nr on line 1a-c and it is taxed at a flat rate, 30% if no treaty rate applies, regardless of whether it would be qualified under the 'resident' system.