Would you please back up your website completely and update the theme to version 6.0.2.
After that please go to X > Fonts and click on the Settings icon at the bottom left section of the screen:
Then set the proper options you need from Typekit:
After that, you will have the font mentioned in the Typekit available which you can select in the font manager and it will show on the front end of the website.
Also, make sure that you set the Typekit options correctly as mentioned in the article below:
https://theme.co/apex/forum/t/extension-typekit/88 (The article is for another plugin but the part talking about the Typekit settings inside their website applies to your case).