I wasn't able to find this in supermarkets in Yokohama but I just came back from a 4 day trip to Fukushima and look what I found in a local supermarket up there!
The ingredient list (which I forgot to take a picture of) listed kuki wakame as the main iingredient and no other types of seweeds were listed. This specific product did not contain agar agar in any form. The main seasonings were soy sauce, vinegar, sesame oil, sesame seeds and kochujang! This particular product was made in Niigata, it was quite good and my husband, who normally doesn't care for wakame, devoured the pack. IIt was definitely cheaper here than in the US, that pack of 180g (6.3 oz) cost me 198 yen ($1.70).
I was over at ou local Sam's Club yesterday and saw large packages of the seaweed salad, which they called Seaweed (Wakame) Salad. First ingredient listed was wakame (not specifying which type), then agar agar, the usual seasoning ingredients, and lots of artificial ingredients (preservatives, food dyes).
So it appears that some brands use agar agar and some don't.