"and the non taken up rights to shares won’t be issued" - Are...

"and the non taken up rights to shares won’t be issued" - Are you so sure? Maybe you are trying to get them for yourself!?

Non-renounceable means not transferable. Not underwritten means there is no-one has made the guarantee that all available shares will be brought. Neither of those tell me "the non taken up rights to shares won’t be issued".

As I can see the closest it gets to saying that is
"Eligible Shareholders may:
(a) take up their Entitlement in full (refer to Section 5.1);
(b) take up part of their Entitlement, in which case the balance of the Entitlement would lapse (refer to Section 5.2); or
(c) allow their Entitlement to lapse (refer to Section 5.3)."

Having said that the document refers to "Entitlement Offer and the Shortfall Share Offer (if any)" on a few occasions, so maybe there is a shortfall share offer. Also, page 18 states "Refund amounts, if any, will be paid in Australian dollars. You will be paid by cheque sent by ordinary post to your address as recorded on the share register." How else would you need a refund other than oversubscribing?

It is pretty mute on how shortfalls and unsolicited over subscriptions will be handled...