Need *Batch* File Conversion feature : Quicktime .mov files to other video formats?

Thank you v much for this inputs. Immediately I have checked the services preferences where it was unchecked before.

And post that when checked in the contextual menu, could see the option of Encode Selected Video Files as shown below -

Also, thanks to "DialAbrain" for his inputs here which also helped me to understand and get back this right context or control-click context menu after following both of your screenshots. 

But one core requirement still there which Apple may not be offering time being. Posting it in next here and also as a new Post in the community. ( "How to convert .Mov files to a more compressed format like MPEG, DIvX etc? " )

Why helpful your answer is - that after seeing your this screenshot, I have realized something like this might be missing in the preferences and I never know "Services" menu can be accessed from that top menu as well ( I saw earlier unconsciously though) . Thank you v much.

Earlier, "Encode Selected Video Files" was not visible here. ( noticed before adding in the system preferences )

Also many thanks to "VikingOSX" for his inputs here with his screenshots.

Though inputs by "DialAbrain" and "Viking OS X" helped me to immediately resolve the appearance of context menu item Encode Selected Video Files and thanks a lot for that, I would like to know further how to convert the .mov files ( either single or as a batch conversion ) to a different compressed video format from finder if it any option is available.

Please note the limited options seen here after selecting the context menu item Encode Selected Video Files.

"H.264", "HEVC" codecs only are the options.

So after choosing H.264 480pixel to convert IMG_3140 Trim.mov, for example, it gives a same .mov output file. ( i.e. IMG_3140 Trim-1.mov ).

Is there any in-built or secured/safe 3rd party method to convert?

I'm confused with VLC interface to choose exactly what to give better compressed file as most times it gives not viewable files though audio ok.

I am not able to add/ insert/ upload images/ screenshots with my posted query. Safari is restarting always. Or This page is getting reset. So trying to insert the images now.

Context Menu items with multiples .mov files selected.

Context Menu items with just one .mov file selected.

None shows Services. > Encode Selected Video Files

What could be the reason?