The two lines you referenced—the mov and the cmp—are independent of each other, but both redundant (though I have a guess as to what the cmp was for). The mov to dx is completely useless on account of never being read before being overwritten in the next loop (the mov to edx). On the last loop, it'll leave the value of [achar] (treating it as a word instead of a byte, as noted by Jester) as an argument to the exit syscall... which takes no argument in edx. So yeah, that's useless.

The cmp is comparing with 0x0D, which is the ASCII code for a carriage return. My guess is that this was at one point used to escape/not print this character because it would (somehow?) mess things up for it. But regardless, it's also useless here. The inc overwrites any relevant flags, and the loop would use ecx by itself anyways, not zf as set by cmp or inc.