Many militaries around the world recruit non-citizen troops, so this is not unusual.
It's desperate and sad not because they are contemplating recruiting foreigners, but it is just illustrative of what a sorry state the place is in.
1. The professional forces recruitment is a failure so far. There are not enough people volunteering, and there are actually stupid counter productive "civil defense" groups cropping up. These stupid groups would probably have no military value in an actual war, and in peacetime it is giving the false impression to people that they are participating in defense related activities.
2. Taiwan wages are amongst the lowest in Asia, the military is no different, who are they going to recruit? More Indians? (The last quote from the Vietnamese person is telling, "if the pay is right...", it is not)
3. Most of the migrants are there due to a labour shortage, especially jobs like construction. If they are full time in the military, then that creates a new job vacancy elsewhere, slowing down the economy by reducing productivity.
4. If they are not full time, then it is again more useless "conscript" type soldiers. The less professionals, the more critical the shortage will be in MOCs like aircraft ground crew, radar operators, maintenance staff, etc. There is no semi-professional reserve like US, Canada and other countries at this time.
5. An idea like this: “There will doubtless be many foreigners who have settled down in Taiwan and made a life for themselves here and who, in the event of an invasion, would be willing to take up arms to defend their adopted homeland,” is just wishful thinking.
Sure, some are willing, maybe even a higher percentage of "native born". However, the overall numbers of people willing to fight is always low because people usually don't want to die.
If hostilities start, are people going to be clamouring to join the military? Maybe there is an initial surge for a short period, but the romance of "defending your homeland" will quickly dissipate once you realize the enemy you are fighting is some medium altitude drone you can't see spamming missiles/rockets.