Using TOP in INSERT INTO statement
And is it correct to assume that the n rows that are chosen from
  table_name2 are completely random records?


When an order isn't specified, it will usually use the sort fields and directions from the design of the primary key of table_name2, but is not guaranteed to.  As Aaron Bertrand said 


  It doesn't really matter what the clustered index is. SQL Server may
  still return the order based on some other index based on a wide
  variety of factors. Creating a primary key on some column DOES NOT
  guarantee that selects with no order by will suddenly come back
  ordered by that column always. Might you observe that most of the
  time? Sure. But that is not the same as a guarantee. I've never seen a
  polar bear on my street but there is no polar bear forcefield that
  prevents it from happening. – Aaron Bertrand♦ Sep 14 '11 at 20:41


It certainly wouldn't hurt to add your order clause in, even if you want them to return in the index order of the PK.

From the tutorial example

INSERT INTO table_name1 (Col1, Col2)
  SELECT TOP n Col3, Col4
  FROM table_name2 
Order By Col1;


Gaaaah.  That's horrible coding. That will order by Col1 ASC of table_name2, even though your SELECT clause isn't explicitly returning a Col1 from the second table. It is NOT ordered by Col3 of the 2nd table aka Col1 of the 1st table. The MS docs for INSERT INTO do not list an ORDER BY clause - the ORDER BY is part of the inner SELECT clause.

It's always better to explicitly specify which table you are inserting into and selecting from.  E.g. this would be a slightly better example.

INSERT INTO
  table_name1 (Col1, Col2)
  SELECT TOP 3
    t2.Col3
    ,t2.Col4
  FROM 
    table_name2 AS t2
  ORDER BY
    t2.Col1 ASC, t2.Col3 ASC, t2.Col4 ASC


After this alteration there's no confusion about what Col1 means (nor the sort order of it). I'd still recommend throwing in a sort order of Col3 and Col4 if Col1 isn't unique for all entries in table_name2, as demonstrated above. You cannot alias the table that records are inserted into (e.g. table_name1 AS t1 (t1.Col1, t1.Col2) as that is not legal syntax for existing versions of SQL Server.

Opinion-based recommendation: avoid the tutorial website that you found.