Even if it's really two "applications" running on the same CPU I don't see how spectre/meltdown would help since it's all about getting read-only access to "forbidden" memory. Clearly they don't need that (they know full well what's in memory), they want to be able to modify it.
In such a situation RowHammer might be used to modify the state of an other program sharing the same RAM in the right conditions but if there's one piece of hardware I expect to be hardened against spurious bitflips it's a space probe. We're talking about radiation-hardened ECC-protected RAM after all.
It also had a branch predictor, however, this line is notable:
> Note that the RSC never speculatively executes prefetched instructions.
This means that the branch predictor only did fetch/decode, and so the chip would not have been susceptible to Spectre, as the pipeline would have been flushed and the correct instructions reloaded as soon as the condition evaluated false, before the branch would have been actually executed.
[1]https://web.archive.org/web/20131004213712/http://zmoore.net...
That was the Pentium 4 not yet in existence so there is no chance of there being an x86 able to be 'Meltdowned' in space. However you are most definitely thinking along the right lines, but I am sure the NASA boffins would have tried all the hacks they could back in 2007. Or maybe the management made sure this was not possible, much like how the Voyager missions were not supposed to go beyond Saturn yet behind the backs on management everyone made sure those spacecraft could get past the edge of the heliosphere.