You can't do this on the table, no, as there's nothing to make UNIQUE on.
What you could do, however, is use a VIEW to enforce it.
Firstly, let's create your table. I assume the columns datetime, should actually be begin and end; I recommend against these names as they are reserved keywords. As such I am calling them DateBegin and DateEnd. I am also assuming that they are date only (no time portion) values and so define them as a date not a datetime:
CREATE TABLE dbo.mytable(ID int primary key,
Value int,
[BeginDate] date NULL,
[EndEnd] date NULL);
And we'll INSERT your first 2 rows, as they are "ok":
INSERT INTO dbo.mytable (ID, Value, BeginDate, EndDate)
VALUES(1, 1, '20210723', '20210724'),
(2, 1, '20210725', NULL);
Now we need to make a VIEW, but we need one row per date. As such you'll want to create a Calendar Table. I'm not going to cover how to create one here, but there are literally 100's of articles, such as there on SQL Server Central: Bones of SQL - The Calendar Table, Calendar Tables in T-SQL.
Once you have your Calendar table, you can create the VIEW below, which JOINs the data in your table to the calendar table. We're going to make it so that the VIEW just returns the columns value and the date. WE're also going to schemabind it; this means we'll be able to add an UNIQUE INDEX to it:
CREATE VIEW dbo.MyView
WITH SCHEMABINDING
AS
SELECT MT.[Value],
CT.CalendarDate
FROM dbo.MyTable MT
JOIN dbo.CalendarTable CT ON MT.BeginDate <= CT.CalendarDate --I assume, despite your schema, MT.BeginDate can't be NULL
AND (MT.EndDate >= CT.CalendarDate OR MT.EndDate IS NULL);
Now we have a VIEW that has a row for each date, and for each value. This means we can now create our UNIQUE INDEX:
CREATE UNIQUE CLUSTERED INDEX MyIndex ON dbo.MyView ([Value], CalendarDate);
Now if we try to INSERT a row that is on the same date and value, we'll get an error:
INSERT INTO dbo.MyTable (ID, Value, BeginDate, EndDate)
VALUES(3, 1, '20210720', '20210723');
Cannot insert duplicate key row in object 'dbo.MyView' with unique index 'MyIndex'. The duplicate key value is (1, 2021-07-23).