OLD TV NUT
Yes, it is evenly spaced lines of dots. Sometimes it's diagonal and sometimes straight across. A little hard to see in the video and depending on how much contrast there is. Of course much easier to see in person.
Doesn't look to me like it moves with the sound. It may be the converter box. I'll have to test with my NTSC gen to rule that out.
Here's another video you may be able to spot it more toward the middle to end...
https://youtu.be/LmjJ_O4L034