Why exactly these six widths?

They cover the common classes: a narrow and a very narrow phone, the telephone in landscape format, a tablet in portrait format, a common desk screen and a wide monitor. 320 pixels is also the width at which the accessibility rule for the flow (1.4.10) applies. The report mentions the values so that a result remains traceable.

Is it enough to just narrow the browser window?

For a first look, yes; for a check, no. The device identifier, touch capability, and screen density stay the desktop's — exactly the traits many pages base their behaviour on.

This translation has not been editorially reviewed yet. The German version is authoritative. Deutsche Fassung →

Which devices get checked — and why shrinking the window isn't enough

It is measured in six profiles: smartphone at 390 and at 320 pixels (the reference width of accessibility rule 1.4.10), telephone in landscape format at 844, tablet at 768, desktop at 1440 and wide at 1920 — each in the real browser with matching device identifier, screen density and touch capability. This is different than narrowing a desktop window.

The difference isn't theoretical: many pages deliver different content when they detect a phone, and CSS queries for pointer precision or touch don't apply at all in a shrunk desktop window.
The higher screen density of the phone profile is also part of the measurement — it helps decide which image gets loaded and how sharp it appears.
Every profile is assessed independently. A good desktop value doesn't make up for a poor phone result.

Deutsche Fassung — mit allen Prüfpunkten dieses Themas