From the documentation of MechanicalSoup (translated, and the bold is mine):
requests-html does is use the pyppeteer library to launch Chromium with the option
--headless and "handle it by remote control".
Chromium is an implementation of open code from Chrome. The
--headless option makes it run without opening any window, but otherwise fully functional (the "exit" of the page in question is rendered in an invisible "virtual" window, but you could even get a screenshot of the result ).
This type of techniques is usually used for testing of web applications (to automate user actions and see that the result is what you want), but
requests-html uses it more for get the resulting DOM that you can then analyze to extract links and other scraping tasks.