How to access a newly mounted DMG from VMWare Fusion (Windows 8.1)?
I don't think this is possible without some special software in the windows vm. The dmg  is analogous to the windows .exe.  In the same way a Mac can not run an .exe, a windows box can not open a dmg.  That being said a software solution like transmac installed in the vm may offer the functionality you seek. 

No personal experience with transmac myself. 

http://www.acutesystems.com/scrtm.htm

Trasmac features:

-Open Mac format disk drives, flash drives, CD/DVD/Blu-ray media, high density diskettes, dmg and sparseimage files.

-Copy files to Mac disks and dmg images.

-Format for Mac and restore disks and flash drives.

-Create, compress and expand (convert to iso) dmg files.

-Built in burner functionality to burn ISO and dmg files directly to CD/DVD/Blu-Ray.

-Read Mac multisession and hybrid CDs.

Good luck.