I can see you have a form coming up so it's possible, however, when we drop the embed code in (mirroring your screenshot) nothing comes up in the video, it just goes blank but no form appears. Our rep has confirmed this too which is why he is working with his dev team to find a solution.
My developer looked at the video you sent and checked the source code on the landing page and he could see there was some customization done on the backend but maybe that wasn't done by you?
Either way - not arguing that you can't get it to work because you were able to for your video - just clarifying that at least in the case for us it is not as simple as dropping in the embed code and we are still waiting on an answer from Wistia.
I still don't know what custom code you mean -- you can look in the Pen and see that there isn't any (except for the code I added later to interact with the Wistia API for the "skip").
If your developer is confused maybe they could contact me at email@example.com. There's no magic. Like I said, it was a 5-minute solution and maybe another 10m to deal with the "skip" functionality. I've never used Wistia before, either, so I didn't have any tech tricks, just their documentation.