Hi @mrudulmo, I was able to reproduce the issue on my local instance. I think you need to add new Schema form for MIME type. It is because only some schemas are available OOTB, here is the documentation.
Background of observed issue:
If you will look under /system/console/mimetypes you will see that *.eps extension is correlated with application/postscript MIME type.

Knowing that, if you will refer to the documentation - application/postscript is already associated with application/pdf schema form. This is why your custom eps schema is not applied.
Solution
You will need to follow below guide additinaly to what you have already configured.
Create new Schema form for application/postscript MIME type and connect it with *.eps extension. This will allow to recognize your custom metadata schema correctly. Assuming your schema for *.eps files is located under image schemas, you have to add below eps node under /etc/dam/metadataeditor/mimetypemappings. This can be done directly from crx/de or from code e.g. you can include it in your crx package. See below screen, with all the details:

⚠️Please be aware that order matters - so your eps node have to be located before pdf node. It's because pdf node is also connected with application/postscript MIME type - so first match will be selected.