You have to set a variable with the command result. This is answered in Windows Batch help in setting a variable from command output, using a dummy for-loop whose loop variable is set from the content of a file.
That would be something like this:
findstr /I "%%a" %MYFILES%\Dir_ALL.txt >%temp%\temp.txt
for /f %%i in (%temp%\temp.txt) do echo %time%;%date%;%computername%;%%i >> %computername%_File.csv
del %temp%\temp.txt
There is a limitation on this: the variable cannot contain multiple lines. However, rephrasing your script fragment as a loop would probably solve that issue as well.
The MSDN article on set
shows some additional features which you can use to control how the data from the file is parsed. Normally it parses the result into tokens separated by spaces. But you can override that using the delims
keyword.