There are some improvements in the "more readable" text, but also some noticeable regressions: "Born premature" is an established turn of phrase. You read it, you know exactly what is meant. "Born early" is not an established phrase. You have to think about it more. It could mean "born early in the morning" or "born before her time" or "born prematurely". You can figure it out, it's not rocket science, but it's a lit…
If you don't have that knowledge retained it's a much larger leap to figure out what "premature" means. you have to understand the prefix (pre = before) and know what "mature" means in this context (not old, but rather "not ready").
This complicates the fact that premature birth also requires a lot of prior understanding (why can a baby be born too early? why is that a problem?)
Perhaps the author could have elaborated a little with plain language... "Born too soon" might be clearer.