Significance of the word "wealth" in Jaravagga
The PTS dictionary says,


  Dhana (nt.) [Ved. dhana; usually taken to dhā (see dadhāti) as "stake, prize at game, booty," cp. pradhāna &amp; Gr. qe/ma; but more likely in orig. meaning "grain, possession of corn, crops etc.," cp. Lith. dūna bread, Sk. dhānā pl. grains &amp; dhañña=dhana -- like, i. e. corn, grain] wealth, usually wealth of money, riches, treasures. 1. Lit. D i.73 (sa˚); M ii.180.; A iii.222; iv.4 sq.; Nd2 135 (+yasa, issariya etc.) Th 2, 464 (+issariya); J i.225 (paṭhavigataŋ karoti: hide in the ground), 262, 289; ii.112; iv.2; Sn 60, 185, 302; Pv ii.610; DhA i.238. Often in combn aḍḍha mahaddhana mahābhoga to indicate immense wealth (see aḍḍha) PvA 3, 214 etc. (see also below ˚dhañña). -- 2. fig. Used in the expression sattavidha -- ariya -- dhana "the 7 fold noble treasure" of the good qualities or virtues, viz. saddhā, cāga etc. (see enumd under cāga) D iii.163, 164, 251; VvA 113; ThA 240.


In summary it means something like "treasure": whether that's money or good qualities or virtues.

Some comments:


It can't mean (wouldn't make sense meaning) literally only 'money' because it says, " If he had learnt to look after his riches in the first stage of his life...,  if he had become a bhikkhu, he could have been an arahat" because though bhikkhus "accumulate virtue" they don't "look after money".
An origin story of the Buddha was that someone (I have forgotten who) prophesied that he would become a world-ruler or a spiritual emancipator (and his father wanted the former which is why he tried to keep him isolated in his palace, unaware of the wide world and of its spiritual needs).
According to what I've read e.g. (The Buddha's Teachings on Prosperity) Buddha doesn't condemn riches for the layperson. Although they're not ultimately or permanently satisfying (which is a reason why he suggests 'renunciation' instead, for monks), but riches are useful and there's some advice in the canon about how a lay person should fulfill their role within society.