This was a really cool concept that I think with a bit more work could be great.
I really like the link mechanic and how it's used to create puzzles. The puzzles were well thought out and decently hard, I had to really think to get through some of them. The design of the Linklings all around was really cool too - reminds me of Lemmings. I really like how creative you can get with shapes when linking as well.
It did take me quite a while to figure out how to get the link mechanic to work. I really wish there was an indication on-screen of when you are/aren't in Link Mode, similar to what you did for the Unlink Mode (which was great). And maybe a sound that plays when a link is made to indicate that to the player. Not knowing when I was linking made some of the inputs very confusing.
Despite that though, really good job. Definitely fits the theme, runs, and plays well.