Well as they are both the exact same laptop, made by acer - get the cheapest one.

But I would suggest you look for one with an amd processor. Cheaper, faster and with better graphics integration.

https://www.amazon.com/Gaming-FreeSync-Display-Editing-GL702ZC/dp/B077GBJCNC/ref...
That will piddle all over the acer machine !

Will you have a biggish screen tv ?
Hooking up with a hdmi cable usually works well. Add a wireless mouse and keyboard and you can just use the laptop as a surrogate base unit.

Been building, fixing and everything else computer wise, professionally, for over 30 years. So yes I do know exactly what I'm talking about

The old amd a10 processor outperformed the intel i7's.
The new Ryzens leave them in their dust !
8 cores versus 4, newer architecture, graphics tied closely to the cpu.

It's a thing of beauty    

And you will also need a good cooling pad. Ideally nobody should EVER be allowed to buy a laptop without also getting a cooling pad. With a serious gaming machine it's crucial. What you have is the same parts that should be in a large airy case with lots of fans, crammed into a tight space with bugger all air circulation.

Cooling gear is NOT OPTIONAL !

Something like this: https://www.amazon.com/HAVIT-Laptop-Cooling-Cooler-Adjustable/dp/B0713PHFRW/ref=...

Also a vacumn cooler would be a good idea:https://www.amazon.com/Temperature-Auto-Temp-Detection-2600-5000RPM-Nintendo/dp/...

I'll say it again - these are NOT OPTIONAL - not if you don't want the laptop to burn up inside a week.

If that kit were in proper case, you'd have a cpu cooling fan and heatsink the size of a brick, at least 2, 4 inch case fans and a lot of air space for it all to circulate in. Assuming you hadn't gone for the recommended water cooling system, that by itself is almost the size of a laptop  

This is what the graphics chip cooling alone would look like in a full size case:


That's a $270 graphics card. Quite how they cram it into a laptop without it melting a hole in the case - is anyones guess.
But basically: there is no such thing as too much cooling

Now you can save nearly $400 by buying a refurbished unit. I DO NOT recommend this for a hi-spec laptop.
It's probably been run too hot for too long with out cooling, and the refurbishment does not appear to include changing any hardware.
So suck it up and buy a new unit

If you need advice on computers CA is the one to go to.

I'm wondering though... Why does one need all that computer when old school Nintendo Roms run on your phone? Are you saying there are other games worth playing? I'm confused. 

So, I’ve thought long and hard, gotten multiple opinions, researched a ton, and in the end I’m going to get this one https://www.amazon.com/dp/B01N6S4A2U?tag=thewire06-20&linkCode=xm2&ascsubtag=AgE... thanks for all the advice, and I will certainly be buying the cooling equipment you suggested.