So I've been looking at this for exactly the same MacBook Pro. I have a setup I really like with an LG 34um95 and a caldigit TS2 dock. One thunderbolt cable (plus the power cable) connects me to the screen, Ethernet, a mouse, keyboard and an external drive.
I can play games on this setup and it's fine but I generally have the settings low and the resolution set below the true screen resolution. An eGPU would be a dream if it was plug and play and a reasonable price but having looking into it the cost is high, it limits you to dated gfx cards in macOS and looks like it could be troublesome to get working.
As an alternative I'm considering a headless Steam in home streaming server running windows and hiding that out of the way in another room. The advantage is it's much easier to upgrade, zero limits on what parts I can use and I can continue to use my setup as I like it now... Uncluttered and portable when required.
Again the cost of building a dedicated gaming PC is high, I'm looking at about £1,000, but spending around £600 to £700 on an eGPU is a bigger risk as far as I can tell. I also have an Nvidia Shield under a TV so a dedicated PC would open up that for proper gaming as well.
I do think eGPU with thunderbolt 3 has huge potential. I just can't see Apple being keen anytime soon.