From JSCript's Wikipedia:
JScript .NET can be used for ASP.NET pages and for complete .NET applications, but the lack of support for this language in Microsoft Visual Studio place it more as an upgrade path for classic ASP using classic JScript than as a new first-class language.
JScript.NET would allow one to write a server side website in something that resembles Javascript. It can allow what the *nix community has with Node.js (server side javascript) on Windows servers (yes I know that there is a Windows port of Node).
If you were after first-class scripting capability, doesn't PowerShell fit the bill?
The thing is, JScript.Net creates an executable file. So you could write a full-fledged program in it and deploy it rather than just a script with PowerShell. Granted, I don't know of anybody who would want to do that, but apparently Microsoft believes there is at least a handful that do.