No share button
This can be caused by ad block software such as "Ad Block" or "AdBlock Plus" working incorrectly.
We're not sure why this happens, but if you follow the steps for Disabling AdBlock on gyazo.com, you should be able to see the share menu normally like this.
Note: We're not sure why but this is a false positive for advertising. The share menu does not contain any advertisements, but there are ad banners shown lower on the page when using the free version of Gyazo. You can block the element individually or consider upgrading to Gyazo Pro to remove all advertisements for you and your viewers.