I guess I'll start from the top. All egpus are just an adapter to pcie x16 and a psu to power a desktop gpu. There is nothing else needed for you. The adapter goes to any port that uses pcie protocols: m.2, mpcie, expresscard, thunderbolt, or a proprietary connection. You'll need to know what port your pc has but yours has tb3 so that's easy. The monitor plugs into the egpu and only a few laptops can use optimus to use the internal monitor. Commercial products will be an enclosure with psu in them but will be more expensive since there's more business operational costs. There are cheaper diy solutions and most just buy an adapter+psu since it's cheaper and forgo the enclosure.
There are multiple commercial products that have been demoed but so far only razer has released one that isn't proprietary and uses tb3. There have been even more in the past that have never went to production so I don't care to talk about them until a release date is said. The other tb3 ones were supposed to come out this year but it doesn't look like it'll happen. I suspect they are facing the same issue as egpus in the past: cost and small market size making it unreasonable to manufacture. Egpus have gotten a bit of news with the release of tb3 because it has a bandwidth of up to pcie 3.0 x4 which isn't too bad of a bottleneck, only 5% less performance on gtx980 pcie scaling tests. Expresscard and mpcie has been used in the past but being limited to pcie 2.0 x1 dropped performance of the card almost in half. But those adapters are cheap like $30 and even a gpu at half the performance is better than what many laptops have.
The msi gaming dock and gaming dock mini I think you are referring to only works on the MSI GS30 and GS32 laptops as it uses a proprietary connection. They have no other egpus and those aren't even sold separately, only with the laptops. The gaming dock is bigger than a mitx pc so it doesn't even make sense to get it. What makes you not interested in the razer core?
Right now tb3 costs a lot though no matter what you do and doesn't make sense cost wise. You can get better performance by not spending money an egpu adapter and just getting a desktop. The nuc wouldn't be used so then just sell that and put that towards the desktop for better results. You can even make a small mitx pc with a full size gpu. The smallest and best value cases I know of are the rvz02, ml08, or node 202 which use stx psus and need low profile or aio cpu coolers. But personally I'd go a bit bigger for a lower cost normal air cooler and atx psu.