@Poemetra Leaving out a couple of options that I'm not seeing (and that you might not be able to find), here's a ranking of the graphics cards you might buy, all from Nvidia:
- 1050
- 1050 ti
- 1650
- 1060 3 GB
- 1060 6 GB
- 1660 ti
Since we don't know what Sims 4 will look like by the time it's out of development, it's impossible to say exactly what card you'd need to run the game with all packs on ultra settings. But we can guess, and our best guess is that the 1060 3 GB is right on the border, maybe being just enough, or not quite. The 6 GB version of a 1060 would certainly be sufficient. Anything lower, and you would likely need to turn your graphics back down to high at some point in the future. Even a 1050, no ti boost, will run the game on ultra now, but the expansion packs are getting somewhat more demanding, and the cumulative impact of all of them needs to be considered as well.
You also mentioned possibly wanting to play other demanding games. Without knowing what those are, I can't tell you what hardware they'd need, but you could list them if you wanted, or else look up their specs yourself.
Again, I'm only looking at one site that I know ships to Japan, and has laptops with U.S. keyboards, and enough variety to be worth searching. I can't tell you what else is out there without doing a lot more research, and even then the language barrier is likely going to be an issue. What I can tell you is that on this one site, the cheapest among all the laptops with a 1650 or above is the first one I linked, with a decent processor and a 1660 ti. I actually got the hard drive size wrong—I mixed it up with a different laptop that I didn't end up posting because I thought this one was better for a slightly lower price. This is the first one again:
https://www.newegg.com/global/jp-en/p/N82E16834235244?Item=N82E16834235244
To get cheaper, you'd have to go all the way down to a 1050 ti. It's still a good card, but not even in the same class as the 1660 ti. This is not the very cheapest option, but it's the cheapest with a combination SSD and HDD. If you had no SSD at all, Windows and many other processes would run much slower, and the option with a single small SSD is only nominally cheaper.
https://www.newegg.com/global/jp-en/obsidian-black-acer-aspire-7-a715-72g-72zr-gaming-entertainment/p/N82E16834316537?Item=N82E16834316537
However, it looks like Amazon will ship to Japan in at least some circumstances. This Amazon help page says it would cost $5 plus $2 per pound, so maybe $17 for a 5.5 lb computer, although you should check on that. (You can email Amazon directly if you want.) It also doesn't include tax or customs fees.
This is the cheapest good computer ($800) on Amazon U.S. that has a 1060; it also has a combination 128 GB SSD/1 TB HDD and a good processor, although it's not as strong as the 8750H.
https://www.amazon.com/Dell-Gaming-Laptop-G5587-5859BLK-PUS-Anti-Glare/dp/B07CD3MRZD
I couldn't find any laptop with a 1660 ti for cheaper than the Acer Predator you already saw, but this MSI, for the same price, has all the same hardware except for a 512 GB SSD:
https://www.amazon.com/MSI-GL63-9SDK-610-i7-9750H-GTX1660Ti/dp/B07QHF3PNH
By the way, last year's Acer Predator, with last year's processor (only slightly weaker than this year's) and a 1060 6 GB, is $1000:
https://www.amazon.com/Acer-Predator-Overclockable-Aeroblade-PH315-51-78NP/dp/B07CTHLX8C
So I guess it really comes down to whether you're taking those other games into account, and how the overall prices look on your end.
I saw the link you found late, so I'll just add this at the end: The graphics card in that one is a 1050, no ti boost, and is weaker than any of the ones I listed. If any of these are within your budget, I think they'd be better options, although MSI is definitely a good brand for gaming laptops.