The lever is not located on the handle, it's located on the spine. It is a separate pivot lever, touching the blade directly.
It pushes the blade forward in range of the assisted opening mechanism, the same way you must push the blade forward with the thumbstud to get it to open with the assisted opening mechanism.
When the blade is open, you can move the lever freely, and it has no effect. The only use of the lever is to push the blade forward. (EDIT)It does not lock the blade in place while it's open or closed. This makes it a useful one handed opening knife.
Assisted opening knives were made to separate themselves from the switchblade category.
The main point in the second video is that assisted open knives do not always retain pressure on the blade, as switchblades do. If the knife is interrupted with the spring assist, it will not continue to open once the obstruction is moved out of the way. With switchblades, once the blade is unlocked, it will continue to push itself open until it is forced closed or locked open.

