When using a flat whip, the best container for the whites is a large flat platter with raised sides. This gives you a generous surface area for moving the whites around and a nice roomy space for manipulating the whip.
To demonstrate, I poured 4 egg whites into a glass pie plate and used the whip shown on the main recipe image.
The whip slides along under the whites on the down stroke and lifts them and incorporates air on the upstroke. In the beginning the air cells are large.
With more vigorous beating coupled with moving the pie plate around, the whites begin to thicken and whiten.
And after a minute or so of whipping the whites look fluffy and cloudlike.
And just a few seconds more of whipping makes your whites stiff enough so you can start beating in sugar.