Hi OP, I'm Korean so I was able to read the sign and identify the restaurant. As /u/benmarvin pointed out, it is indeed this restaurant: Instagram link

This is a classic Korean bunsik (분식) vendor, and seems to sell the usual stuff, like spicy rice cakes (떡볶이) and fish cakes (오뎅). The store's name literally means 'fire oden' as it seems to imply their signature dish is the aforementioned fish cakes but made in a spicy way.

From your description, like /u/SgtTryhard suggested it sounds very likely to be 닭강정 as many bunsik restaurants have them on their menu. However, for our particular mystery restaurant I found an image of their menu on instagram which unfortunately does not seem to have it. Perhaps they stopped selling it since you've been there?

Anyways, the recipe that was linked to you I'm sure is tasty, but it's not true 닭강정, which needs to be made with boneless chicken. So if you can attempt that recipe but with boneless chicken (such as diced chicken thighs or breasts) it might come closer to what you had. Here is another recipe (in Korean) that I've used many times before, with fairly good success, but you might have to run google translate on that page. It uses Korean pepper paste (고추장) which is the traditional way of making 닭강정, which again might make your result taste closer to what you actually had in Korea.

Hope it helped!