Page https://kb.vmware.com/s/article/1308 doesn't mention VMware Server so I scrolled down to the generic section "Manually cleaning a Windows system".
Parts of this page have been updated for Windows 10 but parts have not been updated.
1. I am a member of the Local Administrators group.
2. No VMware services are listed in the Services snap-in, so there is nothing to stop.
3. None of my network adapters have the VMware Bridge Protocol in their list of protocols.
4. No VMware network adapters are listed in Device Manager. I showed hidden devices, which added the Microsoft Kernel Debug Network Adapter but no VMware adapters.
5. Delete folders...
5.1. Yes I had C:\Program Files(X86)\VMware\VMware Server, the only file in it was vmware-mount.exe, and I deleted the folder.
5.2. The page lists the wrong location for application data folders. I had folder C:\ProgramData\VMware\VMware Server containing several files and a subfolder, but I deleted the folder. My individual user's application data folders have some VMware files but they are dated 2014 and newer so I think they're for VMware Player not VMware Server and I didn't delete them.
5.3. The page lists the wrong location for Start Menu program groups too. The correct folder is C:\ProgramData\Microsoft\Windows\Start Menu\Programs but mine doesn't have any VMware files or subfolders in it.
6. My desktop doesn't have any VMware shortcut icons.
7. I hesitate to delete those files because they might be used by VMware Player.
8. I guess these deletions are to be made in Computer Management, Local Users and Groups, but my lists of users and groups do not include those VMware names.
9. Registry keys. I agree, this is where I need to delete something so that Windows will stop thinking that VMware server is installed. But the page doesn't have a section for VMware Server.
Control Panel - All Control Panel Items[*] - Programs and Features still lists VMware Server, installed in 2013, 195 megabytes.
[* I translated コントロール パネル\すべてのコントロール パネル項目\プログラムと機能。 Microsoft's English might differ.]
In regedit, I found two scripting engines for VMware products, and they had VMware Server as their client. I copied the strings for their uninstall commands and they worked. But despite successful uninstallation, the keys remained in the registry, so I deleted the keys.
I found the key for VMware Server itself. I copied the string for its uninstall command but it didn't work, giving the same error message as the original normal operation to uninstall. So I just deleted the key.
Programs and Features no longer lists VMware Server because I deleted the registry key. Programs and Features didn't list the scripting engines in the first place, which might be because their DisplayName keys were blank.
The installer/uninstaller for VMware Server seems to depend on a file remaining in the Temp folder forever. If the uninstaller depends on a file, maybe the file should be stored in the application folder instead of the Temp folder.
I don't know if I got everything.
Did you try and just run the VMware Cleaner from that Knowledgebase article which was linked in Andre's reply above?