Recover deleted VMware virtual disks, i.e. *.vmdk files

As stated above, you can not recover the delete files - they are gone. You had to redeploy the virtual machine and restore from backup.

However, as it appears you deleted the snapshot deltas only, if the base disk (represented by the IBSng_server.vmdk and IBSng_server-flat.vmdk) is intact, you can reboot the machine attaching the original IBSng_server.vmdk file.

This should be sufficient to restart the machine, but with stale data obviously. At this point, you can restore your backupped data on the now-running machine. With this approach you can reduce the time your machine is offline by skipping OS reinstallation.

Deleting a VMDK file is a bit like removing physical hard drives from a server and throwing them away. Too bad.

Fortunately, this kind of thing is exactly what backups are for! Your best bet is to consult your backup/disaster recovery plan and begin a restore from backup immediately.