I think you are looking for image tags, not links ([link] isn't even a BBcode tag).
These urls aren't to actual pictures though, but to sites, so image tags won't work here, you can try either:
http://gyazo.com/f8dc7a48341f40c10858a22163c60915http://gyazo.com/02d1662167ab6b421e03c5f5cc46d36cwhich is:
[url]http://gyazo.com/f8dc7a48341f40c10858a22163c60915[/url]
[url]http://gyazo.com/02d1662167ab6b421e03c5f5cc46d36c[/url]
That does remind me why I disliked Gyazo when I tried it, it gives you links to pages instead of actual images, the image links here seem to be first link + '.gif' and second link + '.png'.
[img]http://gyazo.com/f8dc7a48341f40c10858a22163c60915.gif[/img]
[img]http://gyazo.com/02d1662167ab6b421e03c5f5cc46d36c.png[/img]
That said, I would recommend
puush to everyone looking for a nice screenshot sharing program, which is what I ended up using after my gyazo trial.