Here is proof that you do in fact get gems from capturing. Bunch of people here have mistakenly suggested that because the research guide doesn't show gems a generic reward, that somehow means you can't get it from capturing. This is 100% false.

Generic rewards = Quest Rewards : This is what you boost with Good Luck / Great Luck skills. This is what shows up in the top reward box, on the left hand side. There are other quest rewards in the top box other than this, but the details of how those work is beyond the scope of this post.

Capture rewards = Capture Rewards: This is what you boost with Capture Master skills. This shows up in the bottom reward box, to the right of the break rewards. All capture rewards are specifically marked as such.

Screenshots providing proof: https://imgur.com/a/wtmRG

P.S. I'm sure someone is going to argue you have a higher chance carving gem than getting it from a capture reward. This has never been true in any MH game. Not only is the chance of a capture reward being a gem higher, you get more capture rewards than you do carves on most monsters. It is possible this was changed in World. Anything can be possible, but there is absolutely no reason to believe this is true, and no data anyone has gathered has lent any credibility to this theory. Some monsters have reward that were more likely to be gotten via carving than capturing, but they are the EXCEPTION, not the rule.