Does a fanless mini-ITX like this still require case fans, or is there some way to have a case without fans, possibly with convection cooling?

You could always try and figure out what Calyos is doing in their prototypes.
http://www.calyos-tm.com/calyos-fanless-pc-workstation/

Not exactly an easy solution, but its definitely possible if you can take a massive heat sink and tie it to each component.
They have some information relating to this on their site, but its again really only theoretical. Linus Tech Tips got a chance to review a prototype version in person.

Totally different. My objective is to avoid all that heat piping stuff. I'm asking about the type of board I linked that has its own heatsink already on the CPU. I'm wondering if that could be cooled with convection internally inside the case, not with external heatsinks.

It works if the case allow for some natural convection. Just a sealed box and weeks of Prime95 is a recipe for disaster. The Celeron J3355 has a TDP of 10W.

if your CPU consumes low enough power, absolutely it's possible.

Probably you'd want a vented case to permit fresh air to flow in via convection.

If your case is sealed, then you have much less tolerance.

The only way to know the limits of a custom system is to build it, stress it, and see what happens. With today's apps now allowing throttling based on temperature, i'd say it's safe to experiment.

Any case you can find with the most ventilation holes will give you the best cooling performance. But depending on your tastes, you might trade off the aesthetics.

Theoretically you could just attach the hardware to a piece of plywood and leave it fully exposed, which is maximum cooling efficiency but doesn't do much from protecting it from dropped paperclips & your cat leaning against your memory chips

Thanks. I would probably try to achieve good ventilation without allowing too much dust to settle into the chassis if possible.

The Streacom cases use a copper pipe which attaches from your CPU to the aluminum case, and the case itself is a heat sink. It does command a high premium and it is largely for aesthetic value.

As far as a conventional Mini ITX would go, there would probably need to be a Pico (or modular SFX) power supply, no video card and only M2 SSD for storage in order to accomodate room for a large enough heatsink.

I have a mini-ITX Streacom build. Works great - but I used a 35W TDP CPU.

I have both an SSD and a 2.5" HDD in it, but could not really cool a graphics card as well.

This thread pertains to the feasibility of using a factory-installed CPU heatsink (such as the one shown in the link in my thread starter) in a fanless build. This thread is not about builds using Streamcom or other cases with heatsinks/pipes.

Add a roof and some protective front wall and it should be fine. (See attached image of a side view below.)

I have an Msi n3150i ECO with this abdolutely miniscule heatsink. It's housed in a Jonsbo U1 case along with an SFX psu and old Samsung 3,5" HDD.
The CPU can get to low 70s (Celsius) if I run Prison Architect and a web browser simultaneously. The only fan is in the PSU.

I'd feel quite comfortable using one without any active ventilation if the chip isn't fully stressed, especially if I had only an SSD. Current HDD doubles or triples system power consumption and completely blocks the bottom ventilation area.