What skillet pan to use for making spring rolls wrappers?
I watched the video and after also researching some instructions in Chinese, I have decided that your problem might be more than just pan-related. However, please note, I have discovered that for things that are uncommon, or not commonly made at home (things that are usually store bought or ordered in restaurants), multiple Chinese websites have the exact same word-for-word recipes, so I actually only found 2 uniquely worded recipes.

Difference between your video recipe and other recipes:
The batter flour to water ratio is the same in the video and recipes in Chinese elsewhere. But, the video said to leave the batter for 20-30 minutes but all the other recipes said to leave it for 2 to 3 hours.

Pan:
One recipe said use a flat bottomed non stick pan, the other said to use a flat bottomed pan, but did not specifically say to use a non-stick one. The key is to allow even heat.

Heat:
The recipes I found said to heat the pan until it is warm, then immediately turn it to low, then put the batter in. Also, you should not be using oil.

The sources did say that the hardest part is getting the pan heat right, so you will have to experiment a little with this.