We've been using Closure Compiler for some time now in a .NET-based project.
Initially, we used a simple MSBuild .proj file which directly invoked the Python scripts. For example, we would make deps.js with something like the following:
<PropertyGroup>
<ScriptDirectory>yourprojectname</ScriptDirectory>
<ClosureLibrary>closure</ClosureLibrary>
<CalcDeps>$(ClosureLibrary)\bin\calcdeps.py</CalcDeps>
</PropertyGroup>
<Target Name="Deps">
<Exec Command="$(CalcDeps) -o deps -p $(ScriptDirectory) -d $(ClosureLibrary) --output_file=$(ScriptDirectory)\deps.js" />
</Target>
The actual build was more complex, but still relatively straightforward (assuming you're MSBuild savvy). We simply used different types of item groups for each relevant part of the script invocation.
<Target Name="Build" DependsOnTargets="Init;FindCompiler">
<PropertyGroup Condition="'@(Extern)' != ''">
<Externs>-f --externs=@(Extern, ' -f --externs=')</Externs>
</PropertyGroup>
<PropertyGroup Condition="'@(Define)' != ''">
<Defines>-f --define=@(Define, ' -f --define=')</Defines>
</PropertyGroup>
<PropertyGroup Condition="'@(Compile)' != ''">
<Compile>-i @(Compile, ' -i ')</Compile>
</PropertyGroup>
<Exec Command="$(CalcDeps) $(Compile) -o compiled -c $(ClosureCompiler) -p $(ClosureLibrary) -p $(ScriptDirectory) $(Externs) $(Defines) -f @(CompilerOption, ' -f ') --output_file $(OutputFile)" />
</Target>
This was simple enough that we didn't bother looking for a task, or trying to invest in building our own. Closure is quite a fast moving project, so it's good to be in a situation where you're not overly dependent upon any third party build systems, especially one that looks to be unmaintained (the task you linked).
Now, I've been speaking in past tense because our build system has migrated a bit. Specifically, as our project kept growing it became increasingly important to partition different parts of our script code into modules. Doing this with the out-of-the-box Closure scripts would be quite a nightmare. Thus, we decided to move to plovr (http://plovr.com/), which makes partitioning code into modules very simple. plovr is very actively maintained and was created by Michael Bolin, who literally wrote the book on Closure (also highly recommended).
We still wrap this using the same MSBuild file. Basically, the stuff that we were defining in the item groups moves to a plovr-config.js file, and the invocation becomes much simpler as well:
<Target Name="Build" DependsOnTargets="Init;FindPlovr">
<Exec Command="$(Plovr) build plovr-config.js" />
</Target>
There are some other cool features supported by plovr, like size reports and module graphs, but even without those we're very, very pleased with our current setup.