Typical numbers don't usually have a specific meaning: more often, they're just typical. It's only when you get into gematria and isopsephy, mystic stuff and hidden messages, that the numbers represent something in particular.
9 almost certainly isn't typical; 14 definitely isn't; 7 is typical. The idea isn't that it's any old 14 children, it's specifically seven boys and seven girls. And seven is a very common typical number in Hellenistic Greek thought (that is, 3rd century BCE onwards): seven sages, seven wonders of the world, seven biggest islands, that kind of thing. The seven sages are the earliest group of seven, and it's most probably that they're the prototype for other groups of seven.
But I'll repeat: the number doesn't have a meaning. It's just typical, something that gets repeated -- like children coming in threes in folktales. It's a habit, not a secret message.
The nine years is an interesting thing. I suspect it's a secondary consequence of something else in the story. See, most extant versions of this story don't have the 14 children sent every 9 years: they're sent every year. I've just been on a run through the sources, so here's the summary, with the sources in approximately chronological order:
| Source | No. of children | Frequency |
|---|---|---|
| ps.-Apollodorus 3.15.7 | 7 boys, 7 girls | every year |
| Diodorus of Sicily 4.61.1-4 | 7 boys and 7 girls | every 9 years |
| Vergil Aeneid 6.20-22 | 7 sons | every year |
| ps.-Hyginus Fabulae 41 | 7 boys | once only |
| Plutarch Theseus 15 | 7 youths and 7 maidens | every 9 years |
| Pausanias 1.27.10 | 7 maidens and 7 boys | once only |
| Lactantius Placidus, commentary on Statius Achilleid 192 | 7 boys and 7 girls | every year |
| Servius auctus on Aeneid 6.14 | 7 boys | every year |
| scholion on Plato Minos 321a | 7 10-year-old boys and girls | every year |
| scholion on Iliad 18.590 | 7 youths and 7 maidens | once only? |
| Eustathius, commentary on Odyssey 11.320 | 7 youths and 7 maidens | every year |
You'll notice that none of these is earlier than the 1st century BCE. That puts the numbers squarely in the right period for people thinking of groups of seven.
As for the 9 years that you find in Diodorus and Plutarch, I rather think a clue to that lies in the report given in the scholia on the Platonic Minos. That report also specifies the children's age: seven 10-year-old (deketeis) boys and seven girls. Now, when ancient Greco-Romans specify periods, they count inclusively, so periodic numbers often have to be adjusted up or down by one. I reckon it's likely that the 10-year-old children metamorphosed in some accounts into a story where they are sent to Crete every 10 years -- but, counting inclusively, that would come out as every 9 years.
That isn't by any means rock-solid, but it's reasonable -- reasonable enough that I'd happily propose it in an academic article without fear of criticism.