Yes, the pen/edit icon indicates that you can click it to Edit the template. See template editing in action https://commons.wikimedia.org/wiki/File:CX-TemplateEditor.ogg

So it works as expected. What problem you see here?

@santhosh It does not look super user friendly

• the position of the pencil icon varies - for example, in ruwiki it will be placed well down the template
• the pencil icon is obscured by the text and might not be easily discoverable
  

• it seems that it's not actually required to to click on the pencil icon to start editing the template - two clicks or a double-click will make the template editable
• placing the pencil icon somewhere at the top of a template box may give users a better visual prompt

cc @Pginer-WMF

I agree we should not have a pencil icon there.
The intended designs were captured at T150952: Clarify the access to editing mode when translating templates (which is part of a broader list of improvements to template translation captured in T146760: Fix issues found during user research on template translation prototypes and design reviews )

The example where the pencil icon is almost completely overlapped: