Why can't I save as picture? (Word 2010)

Based on the inclusion of "Edit Points" in the context menu, I'd say that graphic is SmartArt and/or a form of Shape, and not just an embedded image.

Save your picture or SmartArt graphic as a .gif, .png, or .jpg file

You can save a picture or SmartArt graphic in a graphics file format such as Graphics Interchange Format (.gif), JPEG File Interchange Format (.jpg), or Portable Network Graphics Format (.png).

1. Click the picture or SmartArt graphic that you want to save in a graphics file format.
2. On the Home tab, in the Clipboard group, click Copy.
3. On the Home tab, in the Clipboard group, click the arrow under Paste, and then click Paste Special.
4. In the Paste Special dialog box, in the As list, click Picture (GIF), Picture (PNG), or Picture (JPEG).
5. Right-click the graphic, and then click Save as Picture.
6. Type a name for your graphic file, browse to the location where you want to save the file, and then click Save.

Source

You can also save the picture using the following basic steps:

1. Save the document as a webpage

2. Open the webpage and save the picture,