Do you want to add the button in a post (in this case, see this topic) or do you want to customize an existing button in Discourse’s interface?
Yes, but if you want to add a button to Discourse’s interface, that’s something else and it requires programming.
On a side note, the video bothers me because the creator didn’t put any link to the actual code (sites like https://codepen.io are very useful to work on this kind of stuff). It’s fairly advanced CSS and copying it manually from the video will be tedious.
Out of curiosity, I searched a bit on the Internet, and the code is published on their website.
To add to Jay’s reply, I’ll add Make CSS changes on Your Site which may be more straightforward if your only intent is customizing the HTML style on your website.
Last but not least, Discourse forums have an excellent pre-installed plugin named Styleguide that you can enable and that will show pretty much every element of your forum with their current styling:
First, enable the Styleguide page:
Admin panel → Plugins → Styleguide → 
Settings → Check styleguide enabled 
.
Then, you can go to the Styleguide page. Just append /styleguide to your forum URL to see it:
If you don’t really don’t know much about CSS and styling overall, I really advise you to learn the basics before you jump into this button project.