< Ughaibu> That is correct. There is no rule at all about draws or perpetual attack.
Just like nowhere is stated who begins (white or black) there is also no rule about perpetual "check". Which means we have to invent at least two rules.
I like the new rule at brainking which says that white begins, because black is principally reacting to white in Tablut. It fits well in the game.
I don't like the new rule at brainking which makes repetition of moves a draw. Because practically always it is only white who can force a draw, it is a big advantage for white, and it disrupts the game because it distracts black from its target (capture the king) into preventing a draw. It doesn't fit in the game at all, in my opinion.

I suggest the rule should be discarded and replaced by one of the following (or a better one of course!):

A) A threat that will lead to a sure victory may not be repeated more than twice. After that, the offensive side must make another move.
(http://user.tninet.se/~jgd996c/hnefatafl/
hnefatafl.html)

B) The first player who brings about exactly the same position of the pieces for the third time loses the game.

C) When exactly the same position occurs on the board for the third time, white loses the game.