Yup, I wonder how they can guarantee the engine will keep turning for 10 years even. Maybe if everything is sealed in a (very long) lived lubricant that stands the harshness of space?
Stirling engines have a pair of seals that are extremely hard to make durable, and to my knowledge only Whisper Systems has cracked this problem to the point where you won't lose working gas (or seals) in a timespan much shorter than those 10 years. It's a stupidly hard engineering issue, without it there likely would have been far more adoption of the Stirling cycle for production machinery.
That's the usual way things are done. If you buy for instance a simple 5:1 gearbox for industrial use, it will quite likely be a sealed casing 'greased for life'.
Not that I'm disagreeing with you really - mechanical devices have high failure rates. 10 years maintenance-free is a bit of a dream. As a mechanical engineer I'm interested to see whether the Stirling engines involved have radically different scaling to optimise for reliability, or NASA just plan to do the engineering really well.
Of course manned maintenance may be possible - they are touting this technology for Mars bases. Plus robotic maintenance is going to become more of a thing over time.
...that gets you down to something that can generate sound from a heat differential, and you could couple that sound to some kind of transducer to generate electricity. Still a moving part, though.
You probably can't get zero moving parts and yet have it do useful work, but you can get really close I think.
There's some work being done in superfluid discovery which would create the sort of conditions you're looking for but physics discoveries move incredibly slowly and some of the materials are rare or difficult to create. However, that sort of "lubricate, seal, and forget" kinetic system is essential for a lot of surface work in space. Increasingly important on Earth as well.
As a heuristic, the less mechanical parts in any system, the more efficient it is over time.
Ideally, everything that's built is engineered like a spacecraft, because to some extent it is, and is onboard one.