I have removed Wine and all of its files long ago, however recently when I installed Aptik, I could see ~/.local/share/wineprefixes files of size 779MB under the Backup Application Settings in Aptik. What are they, can they be removed, should I remove them? If yes, please let me know how. Thank you.
Yes, you can remove those files since you're not using Wine anymore and aren't concerned with files created by Wine (Assumed from your question). Those are mostly settings files created by Wine while you were using it.
But, before removing I suggest going to that directory and see if any important files are there (very unlikely though). Move them somewhere else if you find any. Then remove the folder using this command
rm -r ~/.local/share/wineprefixes -v
You should now be able to ignore that folder in backup settings.
Note: You can also ignore that folder by unchecking the tick mark in Aptik backup settings window without removing anything.