how to get the date of a file using xp_cmdshell?
This will depend on your regional settings, language, and potentially other settings. 

...
WHERE TRY_CONVERT(date, LEFT(strData,10)) = CONVERT(date, GETDATE());


To avoid anything else from entering the #temp table in the first place, you can use forfiles, which allows you to specify a pattern (eliminating all the extra junk dir adds), specify a date (in this case any file with a modified date >= today), and also only return certain properties of the file (like the date), e.g.:

DECLARE @cmd varchar(4000) = 'forfiles /p C:\...\cmdshell1\ /m *.txt '
  + '/d +' + CONVERT(char(10), getdate(), 101) + ' '
  + '/c "cmd /c echo @fdate"';

INSERT #tmp(strData) EXEC master.sys.xp_cmdshell @cmd;

SELECT * FROM #tmp WHERE strData IS NOT NULL;


Results:

strData
----------
09/25/2018
09/25/2018
...


Your question says you only want the date value output, but that doesn't seem to make a lot of sense to me, since you already know the date, it will be the same on every single row, and all that really tells you is a count (so why not just run a count?). Here's how to pull out the file name with a similar technique (the for /f bit is to eliminate quotes around the @file output, as borrowed from this answer):

DECLARE @d char(10) = CONVERT(char(10), getdate(), 101),
  @cmd varchar(4000) = 'for /f %i in (''forfiles '
    + '/p C:\...\cmdshell1\ '
    + '/m *.txt '
    + '/d +' + @d + ' ' 
    + '/c "cmd /c echo @file"'') do @echo %~i';

INSERT #tmp(strData) EXEC master.sys.xp_cmdshell @cmd;

SELECT strData = @d + ' ' + strData 
FROM #tmp WHERE strData IS NOT NULL;


Results:

strData
--------------------------------
09/25/2018 file1.txt
09/25/2018 file2.txt
...


But I have to agree with Kin, this is much better suited for PowerShell no matter what you're actually looking for and whether it makes sense. xp_cmdshell was turned off by default starting with SQL Server 2005, and that was done for a reason. Let SQL Server focus on the data, and PowerShell and other things deal with the OS layer.