The kink in that logic is that streaming software isn't reliant on beefy hardware - in fact the whole point would be that you can theoretically use your Macbook Air to run a AAA game, it's just an internet dependency. So they can either be building a ~$5000 gaming machine or a cloud streaming service a la Stadia, but having both would be redundant.
Refresh rates are one hardware thing you could still look at, but it would be crazy for them to release an entirely new gaming machine just to run a 120Hz display (especially as streaming retina at 120Hz is probably borderline possible for most internet connections). But GPU and everything is is basically immaterial, other than powering your display. The entire goal of a Stadia-like streaming service would presumably be that any Mac user with any existing Mac device could use it to game on.
You missed my next paragraph:
The interpretation of 'gamer Mac' might have come from hardware assemblers making sample devices to Apple specifications who have no idea of the purpose of the software being developed for the hardware under test.
If we take out the gaming speculation that the article posits we could actually just be looking at a new iMac product if you forget any of the gaming stuff.
What I'm saying is this sketchy rumour has possibly come from someone in the Mac supply chain where at this stage Apple may have requested samples to have been made which must be 'different' enough to make people there report to their contacts in the local press (in this case Taiwan economic daily news).
On the basis that these supply chain guys can only report on orders made for a assembling a product - they won't know anything about macOS, drivers, or APIs.
The current iMac is at the end of a cycle. Although Coffee Lake refresh CPUs could be used to refresh it in March (12 months after the 2019 models came out), there's a more compelling Ice Lake S CPU range due around October which will give hyper threading to i5 as well as i7 SKUs for around 15-20% multicore improvements although single core performance likely won't change much.
The iMac Pro range has had an upgrade to suitable Xeons and could well be the way ahead for 27" iMacs - and that starts at $5k at 2017 set prices. The current iMac can be customised to cost up to $4849 in the US Apple Store. If nothing changed today a US buyer could pick up a 'gaming iMac' for that much and it would come with i9 8 core at 3.6GHz, 64Gb of Apple RAM, Radeon Pro Vega 48, and 2Tb SSD.
If Apple did a bog standard refresh very little would change unless Apple really wanted to go balls out and get the 9th gen i9-9900KS at 4GHz (127w TDP) and throw in some sort of AMD 5700 based GPU. Good luck cooling that lot by the way!
The supply chain surely would not find that of interest as that would be a basic Apple no imagination refresh which they could do any time before WWDC.
A mild form factor refresh sounds unlikely to thrill either as the 27" iMac Pro already exists - bye bye RAM door.
What might have the supply chain guys ringing alarm bells with their news contact would be a new product.
For example - an iMac 24" with 120Hz variable refresh rate HDR DCI-P3 4k display. If it's going to be ready for WWDC (and hence before Ice Lake) as per that speculation article we're looking at uninteresting Coffee Lake refresh CPUs connected to AMD 5500 or 5700 GPU, possibly all SSD (especially if 27" goes all Pro with Xeons as I have suggested) and an iMac Pro style cooling system. Yes, the RAM may be locked in and they may even decide that FaceID could come in as there enclosure would be all new.
But an Ice-Lake based refresh in October this year (with SKUs up to 10 core, 20 threads) would make it very popular, especially if the 27" iMac were to go all 'Pro' but with a lower entry level price thanks to cheaper NAND and CPU discounts from Intel.
Imagine if a 2019 27" iMac Pro started with a 16Gb RAM, 512Gb SSD and AMD 5500? What if the starting price for that was around $3-3.5k?
And under that a 24" iMac with the room (and cooling design of the iMac Pro) to custom build up to $5k worth of CPU and GPU upgrades. This is a Mac that could start with 8Gb RAM, with 256Gb SSD for example. The 24" 4k panel would be fine for many users who wouldn't want to 'upgrade' to a more powerful machine and could start at under $1600.
Now, I've not referenced games here and neither will Apple. As you say just any Mac could stream cloud games if Apple were going that way and that would not affect any Mac with a screen.