However, it looks like you can also subtract the first from the second row
Except for the first three rows, you subtracted the second from the first (also, column, not row). You would have to reword it as "add the third column to the absolute difference between the first and second column".
Given any set of numbers, it's always possible to come up with an infinite number of formulae that give those numbers. So these sorts of puzzles have to be understood to be asking for the simplest formula, and what is "simplest" has some degree of subjectivity. The people writing the test probably didn't think of your formula, and if they had, they probably would have considered it "more complicated".
Once of the more objective measures would be "How long is the description of the formula", and "Multiply the first number by the second number to get the concatenation of the last two numbers" has 95 characters, while "the fourth number is sum of the third number added to the absolute difference between the first and second number" has 113 characters. Not a huge difference, but the first formula wins by this measure.