Yes, you can do video calls on WhatsApp or Skype but italki doesn't have this feature. And for that, you have to exchange your phone numbers.

ADDED: Sorry, I may have given wrong information. Italki seems to have rolled out, or be in the process of rolling out, something called "italki classroom." I don't know anything about it. I'm not sure if it's really out yet because I don't think I've seen anything about it officially. Ah, here it is: https://support.italki.com/hc/en-us/articles/115004548394-New-Feature-italki-Classroom-v0-1-Video-Chat- "We're currently testing the italki Classroom with a select group of students. If you are part of the select group, read on to learn more about the italki Classroom. We want to make sure that the italki works well before rolling it out to everyone on italki. We will gradually increase the percentage of students and countries that have access to the Classroom in the next few months." From the rest of that article, it sounds as if they will be strongly encouraging students and teachers to use it once they feel it is ready. It does not sound as if it will available to language companions.

The italki website does not have a videocall system. Italki is mostly a marketplace to connect students and paid teachers. Students and teachers are expected to make their own arrangements for videocalls. Skype seems to be by far the most popular. In your profile, you indicate which kinds of call you can make, from a list that includes Skype, FaceTime, Google Hangouts, QQ, and Wechat. The teacher does the same. When you make an appointment you say which kind you will use. It is also a social site for meeting people who want to have language exchanges. All arrangements are completely up to you and your partner. You can make Skype videocalls if your partner agrees to give you their Skype address.