No, the translation is correct. Soup usually has meat and/or vegetables in it that we have to chew. So, we "eat" it. We also eat soup from a bowl using a spoon, even if it is just a broth. Sometimes, if I'm at home, I'll drink a broth (nothing to chew in a broth) from a mug but, if company is over, we will eat the broth from a bowl with a spoon. ; )
As non-native english speaker this strikes me very wierd and I guess this is cultural thing only. In other languages (German, Russian, Slovak, etc.) you do "eat soup" as you do with any other kind of food. The comments in this section took me by suprise as this is first time me hearing the phrase. Provided, I did not live in english-only-speaking country.
ps: I know this is 4 years old post but I'm learning german now