My guess is that this is because the post was deleted.
- 18:03:02 question asked
- 18:07:33 suggested edit
- 18:07:47 post deleted by the author
- 18:13:36 suggested edit approved
It looks like the suggested edit review code doesn't check whether the post has been deleted. The logic around the Improve button however does, because it hooks onto the normal edit logic. Since you do not have enough reputation to view this post, you aren't allowed to edit it either, so you don't get an Improve button.
This isn't the only case when you don't get an Improve button. The common case is for a tag wiki, if you have the privilege to review tag wiki edits (5k rep on graduated sites) but not to edit tag wikis without supervision (20k rep on graduated sites).
Servy has enough reputation to view (and edit) deleted posts, so he could have edited the post directly, so he got an Improve button.