I'm not convinced because as the article says, it's not realistic to recycle many kinds of plastic, and because I don't see the harm in safely burying garbage. In my city there is an old landfill which has now been covered in dirt and turned into a park, with a sledding hill and a bike park. If you didn't know better, you wouldn't even be able to tell it was a landfill before, and if properly managed none of that garbage will ever leak out - the city uses well water and has had no problems with contamination from the landfill.
If it is less energy intensive to create new plastics rather than recycling (which seems to be the case), why not just safely bury the old plastics and make new ones, it should be better for the environment anyways. Of course you should try to reduce and reuse before throwing out plastics, but if you have to get rid of them landfills seem reasonable.