This is not a "definitive answer" by any means, but I think it gets to heart of the question.
"Does it have to be exactly 14.0 ... would anyone notice 13.9/14.1?"
Most likely, you wouldn't notice immediately.
Combustion is a simple chemical reaction, and like a lot of chemical reactions, the accuracy of the variables is logarithmically beneficial (i.e. the difference between 45% and 50% is much greater than the different between 90% and 95%). So if your "perfect" AFR was actually 14.0563, the driver would likely not see a major difference 14.0/14.1 and may not even notice 13.9/14.2... but the difference would shown over time with precise investigation.
"How accurate does it need to be?"
As accurate as possible.
As we know, there aren't too many variables in the combustion process, but each of them make a considerable difference. The more accurate the EFI system can be, the better burn you can achieve, and the more you can reduce wear and buildup, and better control emissions. As noted above, the impact of each variable adjustment reduces as you approach perfection, but its ideal for all outcomes if you could hit perfection.
Basically, the more precisely you measure, the more you will see any benefits from the fine-tuned adjustments, ad infinitum. As for how precise you actually need to be, that is most likely dictated by EPA (or similar) emissions guidelines. However just like the benefits of adjustments, the emission/environmental impact is logarithmic. So they will set the bar much lower than "perfection".
So I'd say they "have" to be as accurate as they are currently to comply with regulations (which is not to say that they dont require higher precision in the future).
If you want to know how accurate is beneficial from a performance standpoint, you'll probably have to ask manufacturers or companies like pro race tuners that are dealing with ultra-precise benefits. (The prototype race divisions for companies like Audi have literally spent hundreds of millions of dollars on R&D to get maximum benefit out of every possible angle.)
Finally, to use your analogy of the computer CPUs, the difference between a "low/high-quality" ECU is probably more the speed that it samples and adjusts more than the precision. A CPU from the 60's can do the same math as a CPU from today, it'll just take WAY longer to do it.
Again, this is all just a theoretical, logic-based, answer.
As Paulster2 points out, in production ECUs the accuracy is very likely to vary between manufacturers because of the programmers/engineers particular needs/wants. Even, as he pointed out, some may use Farenheit while other Celcius - very different scales. The same is true with the accuracy requirements they request.
I don't have much knowledge when it comes to flashing or custom programming ECUs, which is what I think you're getting at. I would assume that as with computers there will be lower level code areas that can't be adjusted (or at least they would be a HUGE amount of work and effort if they are possible), and therefore you'll need to work within those confines.