I read that there is an SR associated to this question and it's being worked upon by a support professional. To avoid duplication of efforts, I would request you to continue the troubleshooting in the SR.
I have tagged the SR number along with the issue description for the reference of the support engineer as well.
Once the issue is fixed, I would request you to post the resolution steps here in the community for the benefit of the wider audience here.
Thanks for posting the reported behavior in PSC :)
I tried to replicate the behavior with the custom control as you have shared in the screenshot. However, I am able to see the print functionality working in Safari and chrome browser using Pega 7.2.2. Refer the attached screenshots for your quick reference showing the print popup and log statement in browser console. Only difference being in Chrome, the print view is displayed. Did you mean that this is not working?
Since Support request is raised, you can track the progress on this SR number mentioned.