More information here: https://blest.co.jp/eng/faq/ This seems to be intended for PP/PE which is basically a long-chain hydrocarbon anyway, but does make up the bulk of plastic use. It seems to be a very stereotypically Japanese product.
The current wisdom is that PP is one of the least problematic plastics wrt to leachate contaminating the contents. HDPE is also fairly well regarded. In theory LDPE is also considered 'food safe' but if you can smell the plasticizers evaporating off of LDPE (which I absolutely can) then what's it doing to your food? I read something about PE in the environment recently but I can't recall if it said it was the hardest…
It's more likely you're smelling unpolymerised ethylene. LDPE itself doesn't require plasticisers --- it's already extremely flexible without them.