The video is demonstrating parametric searches, whereby the user on the front end can narrow down the results being displayed by selecting criteria in the dropdown select boxes, is that what you are trying to achieve?
Here is the documentation to do that:
https://toolset.com/documentation/user-guides/front-page-filters/
Let's say you are displaying standard posts, and you want to allow your users to filter them by category. You want a dropdown box where they select their category, and you want them to be able to select multiple categories.
So, you make a new parametric search View which will display posts.
I'm going to choose "AJAX results update when visitors change any filter values" so that the results update straight away when the user makes a change.
Now for my filter, which I will add with the New filter button when my cursor is between the wpv-filter-control shortcode tags.
I'm going to filter by categories. See the attached screenshot where you can see you have options to display your category terms in as radio buttons, checkboxes, a select box, or a multi-select box.
I can then add a content template to the Loop output section to manage the display of my posts in this search list.
Now, if you are referring to the appearance of the select box (or multi-select box), then that is determined by your theme (or your OS if the theme makes no attempt to style them).
As you can see here (hidden link), a multi-select box normally displays a list in a box. Views outputs the required HTML but doesn't make any attempt to style the results.
In your View you have the option to add custom CSS (and/or JS). If you are not happy with how your theme styles the multi-select you can add your own styles, or you could try adding a JavaScript utility to alter the appearance and functionality (searching google will yield many).
