The simplest way (by sticking with AMPScript) is to use a lookuprows to get all your entries, and then use a FOR with IF ELSE statement. This will only work though if you have a universal identifier in the data. E.g. I usually use a column named 'secret' that defaults to a value of 1.
If you do not already have a field like this, what I would recommend is first to add a nullable field named 'secret' with a default value of 1 to 'PlayTogetherWinTogether_Entries_Main'. Then you can either create a SQL Query to update the value or export and import with the update made in excel or similar editor.
SELECT p.*, '1' as secret
FROM PlayTogetherWinTogether_Entries_Main as p
Then select the target DE as 'PlayTogetherWinTogether_Entries_Main' and update type as 'Update'.
Below would be sample AMPScript:
%%[ VAR @count, @today, @rows
SET @count = 0
SET @today = Format(Now(), "MM d, yyyy")
SET @rows = LookupOrderedRows('PlayTogetherWinTogether_Entries_Main', DataExtensionRowCount('PlayTogetherWinTogether_Entries_Main'), 'secret', 1))
FOR @i = 1 to Rowcount(@rows) DO
SET @entry_date = Field(Row(@rows, @i), 'entry_date')
IF FORMAT(@entry_date, "MM d, yyyy") == @today THEN
SET @count = ADD(@count, 1)
It is not as efficient as ROWCOUNT and LookupRows, but it should do the trick.
I have not tested the sample script, so if it throws an error, let me know and I will adjust accordingly.