On the plus side, they have a sensible ballpark estimate for New Zealand (if anything, it's likely on the low side).
But there's a problem with the infographic.*
Yes, if tobacco use had no associated health costs, New Zealand would have an extra NZ$350m in real resources floating around for other uses,** and a loss in utility to smokers who enjoyed smoking. But if we magically made smoking disappear, the government would take a very large fiscal hit: tobacco excise revenues utterly dwarf tobacco-associated healthcare expenditures.
You can view tobacco's health costs as representing forgone government spending in an "if only there were no smoking" sense IF you're willing to assume that, were smoking to disappear, government would increase other tax rates sufficiently to make up the lost tobacco excise revenues and to compensate for the added burden on the superannuation system (net of increased tax revenues from smokers, who tend to be further down the income distribution and consequently more likely to be net tax consumers than tax contributors). Or if you're willing to assume a counterfactual where smoking doesn't have health costs. Neither is quite as simple as "no smoking = more school construction".
* Theorem: there's a problem with every infographic except perhaps those made by @Keith_Ng.
** I'm going to stick with Des O'Dea's numbers here, which had it at $350m, not the NZ$250m the infographic cites.
HT: NBR who, surprisingly, forget that tobacco users pay excise.