This confusion is part of the problem. I've been watching this space a bit, and it tends to be that all types of energy from waste schemes are sometimes advertised as "bioenergy" or "like bioenergy" or "renewable".
To actually evaluate these, one relevant factor is what waste we are talking about. If the source is plastics then of course the more accurate term would be "fossil fuels", because that's what plastics is usually made from.