The blog is from 2013 so parts of it, like the reference to a 256mb VRAM graphics card, is out of date! It's overall point is still relevant though: composition is better than large images.
You could go a lot further with large images on modern systems, and unified memory systems are more prevalent these days (where there is no separate VRAM and the GPU re-uses system memory, perhaps with an additional dedicated cache). However it still won't scale: no matter how many gigabytes of memory you're willing to use, composition can extend to essentially an unlimited extent, whereas a single drawn image will exhaust memory at a far smaller size, so it imposes tighter limits on the level size. Then there's the fact you have to split everything up in to tiles to work around the maximum texture size (4096x4096 tiles for best compatibility) which is inconvenient. A single tile at 4096x4096 is about 67 MB in memory. If you make a 10x10 grid of them (approx 40k x 40k pixels) you have already used well over 6 GB of memory, so your game will probably already crash on systems with 6GB RAM or less, and that's not including the memory requirement of everything else in your game. With composition you could make a same size level probably well within 500 MB RAM. It would probably render faster too as there'd be less pressure on GPU memory.
Realistically for broad compatibility I'd avoid going over 1 GB RAM for the background alone, which as you noted limits you to about 4x4 tiles of 4096x4096, or approx 16k x 16k pixels. I suppose that could be enough for some games. So perhaps it is a somewhat more viable option these days within reasonable limits. However I wouldn't be at all surprised if it runs poorly, especially on weaker devices; if it's at all possible to achieve the same by composition, it's far more efficient, both on memory use and runtime performance. It also depends on how willing you are to have demanding system requirements for gamer-style GPUs with loads of dedicated memory, or compatibility with mobile devices and general web browsing.