1. Without knowing the screen resolution, it's really not possible to make an appropriate recommendation. The ones linked are 1080p so we will assume thats the desired spec.
2. The entry point for laptop gaming is about $850 ... with a budget of $1,000 handling "any game" is just not possible. At 1080p, the entry point if you will is the 1060 for those looking for 60 fps. ... Witcher 3 comes in at a decent 58 fps. The mobile version is a bit slower.
3. The 3 GB 1060 drops down to only 56 fps...but the 1050 Ti takes a precipitous drop down to 36 fps with the 1050 only losing another 4 fps to 32. Again, the mobile versions are a bit slower... so expect to be < 30 fps.
4. You will note that when you go down the spec list for those 2 lappies, at the stuff you don't see in the large type headline... things not lookie so well.
The Giga has 16GB of RAM, a 7200 rpm HD but a 2Gb 1050 GFX card ... The Acer ups the card to the Ti but cuts the RAM in half and supplies a 5400 rpm HD.
5. If he wants to get what he says he wants, he's in $1000 territory. You can get a custom built lappie w/ i7-7700HQ, 16 GB, GTX 1060, no HD or OS for a MSRP for about $1030, delivered. Resellers are not permitted to advertise proces below a certain 'floor' but once you get them on the phone you can negotiate and agreed upon price... which Id expect to be maybe $950 - $980 or so. Add in ya OS ($90) and a 1 TB 7200 rpm SSHD ($68) that you buy and install yaself will bring ya up to just over $1100. That's an extra $130 for almost double the performance.
https

/lpc-digital.com/product/sager-np7850-clevo-n850hp6/
15.6” Full HD (1920 x 1080) Clear IPS Matte Display
7th Generation Intel® Core™ i7-7700HQ (6M Cache, up to 3.80 GHz)
NVIDIA® GeForce™ GTX 1060 GPU with 6GB GDDR5 NVIDIA PASCAL (3 times the VRAM, almost twice the fps)
No OS - Drivers & Utility Software Only
16GB Dual Channel DDR4 PC4 2400MHz Memory (2 x 8GB) ($85 upgrade from 1 x 8GB)
No M.2 SSD
No Hard Drive/SSD
Intel® Dual Band Ultra Wireless - AC 8265 M.2 + Bluetooth 4.2
Full Range AC-in 100~240V, 50~60Hz, 180W AC autoswitch Adapter
NP7850 Smart Li-ION Battery Pack (6 Cell, 62.16Wh)
LIFETIME Limited Labor and 1 Year Premium** Parts Warranty
Free Shipping
Cash Price: $1,036.93 (minus any negotiated discounts see https

/lpc-digital.com/faq/)
I should note that I have bought lappies configured with no storage and no OS from Cleco resellers before. I have been a customer going on 12 years and they have even shipped me parts to do repairs. I do not know if they will extend this courtesy to someone for which they can not judge ones ability to do the work. Usually, once ya take the bottom panels off ya void warranty. So you may have to shop resellers to see who will "bite". perhaps they'd let you ship them the drive or perhaps your fiend will want to spring for an M.2 SSD
PCPartPicker part list /
Price breakdown by merchant
Storage: Seagate - FireCuda 1TB 3.5" 7200RPM Hybrid Internal Hard Drive ($68.06 @ Amazon)
Operating System: Microsoft - Windows 10 Home OEM 64-bit ($89.89 @ OutletPC)
Total: $157.95
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-07-28 00:52 EDT-0400