I thought the 'Queen' in Chaturanga was a Ferz, (1 step diagonal), not a Wazir (which steps orthogonally). Note thatShatranj is a very boring game, with an excessively high draw rate. Chaturanga might be a bit better, because I believe the promotion rules are different there. (In Shatranj you can only promote to Ferz, which is barely stronger than a Pawn.)
If you like that type of slow game, Makruk (Thai Chess) would be a better choice. It does away with the worthless Elephants (which can only visit 8 squares out of the 64), and replaces it by a more interesting piece.
Chaturanga is the earliest Form of chess. Most pieces move in the same way as usual, with the exception of Queen and Bishop (here wazir and elephant). It is interesting in the way that there the pieces are weaker, so that the king can come out earlier and play an active role, and pawns and pawn structures become even more important, since the pieces often don't have the power to corner the opponent's king on their own.
So this more "basic" kind of chess allows you to unfold the kings', pawns', rooks', and knights' full potential, since there is no omnipotent queen that can at any time come out of nowhere and check your king while simultaneously beating an unprotected piece.
So I think, Chaturanga is a nice way for beginners to learn how to use the less strong pieces well.
unfortunately , there is no website like chess.com for Chaturanga, so it's (at least according to my knowledge) impossible to play Chaturanga online against thousands of people. Therefore it would be very nice if chess.com made it possible to play Chaturanga here.
If other people are also interested, please comment to make the administration aware of it.
Thanks