Using transaction on a single update statement

I understand that this is wrong because transaction is used when you want to update multiple tables.

Not necessarily. This involves one table only - and just 2 rows:

--- transaction  begin

BEGIN TRANSACTION ;

UPDATE tableX 
SET Balance = Balance + 100
WHERE id = 42 ;

UPDATE tableX 
SET Balance = Balance - 100
WHERE id = 73 ;

COMMIT TRANSACTION ;

--- transaction  end

Hopefully your colleague's code looks more like this, otherwise SQL will issue a syntax error. As per Ypercube's comment, there is no real purpose in placing one statement inside a transaction, but possibly this is a coding standard or similar.

begin transaction  -- Increases @@TRANCOUNT to 1
update table whatever with whatever
commit transaction  -- DECREMENTS @@TRANCOUNT to 0

Often, when issuing adhoc statements directly against SQL, it is a good idea to wrap your statements in a transaction, just in case something goes wrong and you need to rollback, i.e.

begin transaction -- Just in case my query goofs up
update table whatever with whatever
select ... from table ... -- check that the correct updates / deletes / inserts happened
-- commit transaction  -- Only commit if the above check succeeds.

Perhaps the transaction was included due to prior or possible future code which may involve other data. Perhaps that developer simply makes a habit of wrapping code in transactions, to be 'safe'?

But if the statement literally involves only a single update to a single row, there really is no benefit to that code being there in this case. A transaction does not necessarily 'lock' anything, though the actions performed inside it may, of course. It just makes sure that all the actions contained therein are performed all-or-nothing.

Note that a transaction is not about multiple tables, it's about multiple updates. It assures multiple updates happen all-or-none.

So if you were updating the same table twice, there would be a difference with or without the transaction. But your example shows only a single update statement, presumably updating only a single record.

In fact, it's probably pretty common that transactions encapsulate multiple updates to the same table. Imagine the following:

INSERT INTO Transactions (AccountNum, Amount) VALUES (1, 200)
INSERT INTO Transactions (AccountNum, Amount) values (2, -200)

That should be wrapped into a transaction, to assure that the money is transferred correctly. If one fails, so must the other.