The original research that produced this was done in a collaboration between the University of Glasgow and the University of Oslo, and UoG details it here. While the Glasgow part is available here, the part we are interested in is available here, but is $30.
From the summary, it looks like the comparison is between the cost to produce the plastic used in vinyl, CDs, cassettes, etc, for the peak year (when the format saw its largest annual sales) and the cost to store and transmit the streaming music. It appears that no accounting for population was made - so the fact that more people are around to listen to music today is not factored in to the increased pollution shown - i.e. environmental impact is not per play, but population wide.
Further, while the ecological cost for the streamed music accounts for all expenses from the servers it is stored on to the listener's ears, the cost of the physical distribution options only accounts for the production of the plastic (and maybe the actual "stamping" of the LP, CD, cassette), but does not include distribution or energy cost of playback.
And lastly, it appears that the article assumes that the energy being consumed is non-renewable. The environmental cost of producing plastic and manufacturing it into storage media is non-trivially polluting and while efforts are made to reduce that impact, it is so far not possible to reduce it in the same way that using renewable sources of electricity can reduce environmental impacts.
It is unclear where in the chain the cost of storing music for streaming begins - does it include manufacturing impact for CPUs and hard drives, etc, or only the operating costs of keeping them operational (including cooling)? Where does the cost end for manufacturing media? Bulk plastic production? Stamping? Transport? Playback? And where does it begin? Mining the petroleum? Does it include manufacture of the machines doing the stamping (which would be required for an apples to apples if they included the cost of manufacturing CPUs and hard drives)? These answers are only available in the $30 paperback book published by the author of this part of the study, which seems, well, a bit out of the ordinary, especially considering that the first half of the study provides it's methods and data freely. But the upshot is that without dropping $30 (or $16.19 for the Kindle edition), this is the best supported answer I can provide.
I'd also caution that the research's close association with Record Store Day should call into question the pro-physical media conclusions it draws.