Batch script doesn't run, although its code runs in CMD

There are the following issues in your code:

• in batch files, for meta-variables must be preceded by two %-signs in contrast to one in command prompt (cmd), hence change %a, etc., to %%a, etc.; otherwise, a syntax error arises;
• you could avoid filtering out the headline of the output of wmic by findstr /V when using the skip=1 option of for /F;
• instead of the property Name I recommend to use DeviceID, according to this Super User thread: What is the difference between properties Name, Caption and DeviceID (when executing wmic LogicalDisk)?;
• not sure what drives you want to query, but perhaps you want local disks only; if so, add the clause where "DriveType=3"; refer to this Microsoft article: Win32_LogicalDisk class;
• creation of the temporary VBScript script should happen inside of the if condition where it is called as well in order to avoid pointless file write activities;
• you are appending to the text file in every loop iteration, but you never initialise an empty file at the beginning; perhaps this is the intentional behaviour, but I do not think so; anyway, you could do the redirection once for the whole for /F loop, either (over-)writing (>) or appending (>>), as you prefer;
• the pipe into the type command is useless, because type does not accept any incoming data anyway; I guess the | symbol should have been replaced by &; nevertheless, the type command does not make sense in the loop, I think it should be executed after the loop instead to display the complete collected data once;
• the echo( could be removed as it just writes a blank line to the console;
• at the end the temporary VBScript file should be cleaned up;

Correcting all these things lead to a batch script like this (I do not write it all in a single line for readability):

> "C:\test\test2.txt" (
    for /F "skip=1 tokens=1-3" %%a in ('
        wmic LogicalDisk where "DriveType=3" get DeviceID^,FreeSpace^,Size
    ') do @(
        if not "%%c"=="" (
            > "%TEMP%\tmp.vbs" echo WScript.Echo "%%a" ^& " free=" ^& FormatNumber^(CDbl^(%%b^) / 1024 / 1024 / 1024, 2^) ^& " GiB" ^& " size=" ^& FormatNumber^(CDbl^(%%c^) / 1024 / 1024 / 1024, 2^) ^& " GiB"
            CScript //NoLogo "%TEMP%\tmp.vbs"
        )
    )
)
type "C:\test\test2.txt"
del "%TEMP%\tmp.vbs"

The whole approach could be improved though:

• the temporary VBScript script could be written once rather than per each for /F loop iteration; for this to work you need to pass the variable values as command line arguments; consult this thread to learn how it works: Using command line arguments in VBscript;
• using echo to write the temporary VBScript file requires lots of escaping, like ^&, for example; to avoid this, we could place the VBScript code in a block that is prefixed by ::::, which is seen as an invalid jump label by the batch file interpreter, and they could even be skipped by placing an exit /B just before them; this block can easily be extracted by findstr, and the colons can be removed by for /F;

So this is what I mean:

> "%TEMP%\tmp.vbs" (for /F "tokens=* delims=:" %%z in ('findstr /B "::::" "%~f0"') do @echo/%%z)
> "C:\test\test2.txt" (
    for /F "skip=1 tokens=1-3" %%a in ('
        wmic LogicalDisk where "DriveType=3" get DeviceID^,FreeSpace^,Size
    ') do @(
        if not "%%c"=="" CScript //NoLogo "%TEMP%\tmp.vbs" "%%a" "%%b" "%%c"
    )
)
type "C:\test\test2.txt"
del "%TEMP%\tmp.vbs"
exit /B

::::If WScript.Arguments.Count < 3 Then WScript.Quit 1
::::WScript.Echo WScript.Arguments.Item(0) & _
::::    " free=" & FormatNumber(CDbl(WScript.Arguments.Item(1)) / 1024 / 1024 / 1024, 2) & " GiB" & _
::::    " size=" & FormatNumber(CDbl(WScript.Arguments.Item(2)) / 1024 / 1024 / 1024, 2) & " GiB"

You could even avoid a temporary file holding the VBScript code when applying the technique demonstrated in this thread: Is it possible to embed and execute VBScript within a batch file without using a temporary file?
(Refer also to these Microsoft articles: Using Windows Script Files (.wsf), and How Come You Guys Don’t Use .WSF Files?.)

<!-- :Batch script section
> "C:\test\test2.txt" (
    for /F "skip=1 tokens=1-3" %%a in ('
        wmic LogicalDisk where "DriveType=3" get DeviceID^,FreeSpace^,Size
    ') do @(
        if not "%%c"=="" CScript //NoLogo "%~f0?.wsf" "%%a" "%%b" "%%c"
    )
)
type "C:\test\test2.txt"
exit /B

---- WSF script section -->
<job><script language="VBScript">
    If WScript.Arguments.Count < 3 Then WScript.Quit 1
    WScript.Echo WScript.Arguments.Item(0) & _
        " free=" & FormatNumber(CDbl(WScript.Arguments.Item(1)) / 1024 / 1024 / 1024, 2) & " GiB" & _
        " size=" & FormatNumber(CDbl(WScript.Arguments.Item(2)) / 1024 / 1024 / 1024, 2) & " GiB"
</script></job>

And here is yet another approach that does not use a temporary VBScript file, applying the method illustrated in this thread: HTA & Batch Hybrid, passing variables from BATCH section. The disadvantage of this is brief flickers of HTA windows appearing and disappearing.
(Refer also to this Microsoft article: HTML Applications (HTAs).)

<!-- ::Batch script section ----
> "C:\test\test2.txt" (
    for /F "skip=1 tokens=1-3" %%a in ('
        wmic LogicalDisk where "DriveType=3" get DeviceID^,FreeSpace^,Size
    ') do @(
        if not "%%c"=="" set "DeviceID=%%a" & set "FreeSpace=%%b" & set "Size=%%c" & MSHTA "%~f0"
    )
)
type "C:\test\test2.txt"
exit /B

---- ::HTA script section -->
<script language="VBScript">
    Set Env = CreateObject("WScript.Shell").Environment("Process")
    Set StdOut = CreateObject("Scripting.FileSystemObject").GetStandardStream(1)
    If Not Env("DeviceID") = "" Then
        StdOut.WriteLine(Env("DeviceID") & _
            " free=" & FormatNumber(CDbl(Env("FreeSpace")) / 1024 / 1024 / 1024, 2) & " GiB" & _
            " size=" & FormatNumber(CDbl(Env("Size")) / 1024 / 1024 / 1024, 2) & " GiB")
    End If
    Set StdOut = Nothing
    Set Env = Nothing
    Close()
</script>