The CodePen "Responsive Table 2.5" further builds on that example and tackles that exact problem you mention (by including the heading of what each cell represents)
If you're putting the heading in each cell, it kind of defeats the purpose of using a table to begin with, no? If I was so painted into a corner by mobile support and refused to make scrolling friendly (e.g., by pinning the left column), it sounds like just not using a table in the first place is a much better solution.