how to force close apps without pressing home button

On what iPhone model exactly?

Why don't you want to press the home button?

On iPhones running iOS 11, you can tap and hold on the left edge of the screen until an app appears and then drag it towards the center of the screen to bring up the App switcher. Then just swipe the app up and off the screen to close it.

How does anyone do this with an iPhone X?

It is explained in the support document the OP linked from.

iPhone X

1. From the Home screen, swipe up and pause.
2. Firmly touch and hold the app, then tap . You can also swipe up to close the app as soon as you see .

With Assistive Touch you can use a virtual home button instead of a physical one.

How does anyone do this with an iPhone X?

If you really have an iPhone 4 as indicated in your profile, you are going to have to press the home button, as that is the only way to get multi-tasking view of apps to close them.