If a US resident (not citizen) only works outside of the US (remotely), and resides in the US for the whole year, do they have to file taxes?

A resident alien for tax purposes in the United States is an individual who meets either the green card test or the substantial presence test. 

1. Green Card Test:

   • If you are a lawful permanent resident of the United States at any time during the calendar year, you are considered a resident alien for tax purposes.
   • Having a green card (officially known as a Permanent Resident Card) grants you this status.

2. Substantial Presence Test:

   • If you do not have a green card but spend a significant amount of time in the U.S., you may still be considered a resident alien.
   • The substantial presence test considers the total number of days you were physically present in the U.S. over a three-year period.
   • To meet the substantial presence test, you must be present in the U.S. for at least:
     • 31 days during the current year, and
     • 183 days during the three-year period, counting:
       • All days present in the current year,
       • 1/3 of the days present in the first preceding year, and
       • 1/6 of the days present in the second preceding year.

if he meets either test, he needs either an ITIN or SSN to file his return. As a resident alien he is taxed in the US on his worldwide income. 

If your father is a "US person" for income tax purposes, he must file a US tax return and pay US tax on all his world-wide income.  If he also pays tax overseas, he can claim a deduction or credit for foreign taxes paid, that will offset some of the US tax.  A US person is a US citizen or green card holder anywhere in the world, or an alien who is living in the US and passes the substantial presence test. 

@vipergts_david ,  having read through the thread and agreeing with my colleagues @Mike9241  and @Opus 17 , I would just to add the following:

(a) work that is performed  while in the USA is considered US sourced for purposes of  US taxes. Thus  the income from "remote work" is US sourced for purposes of US taxes  ( both federal and State )

(b)  because  this income is active  income (  but without W-2 , i.e. no withholdings ),   he will have to recognize this income as "self-employment " -- schedule-C.  This will also mean that he will be liable for  SECA taxes   ( equivalent to FICA --- Social Security and Medicare -- at 15.3% on most of the income ).  Depending on the income level, it may be worth  considering  making  estimated tax payments for both Federal and State , just to avoid  interest and penalty charges.

(c)  depending  on the  country where he is from ( i.e. a citizen of ),  any taxes paid  to that taxing authority may be eligible for   tax credit  / deduction etc. to reduce the double taxation bite.  Note that this would mean that  the US sourced income may have to be resourced by treaty

(d)  Till meeting the SPT ( substantial presence test ) he will be a Non-Resident Alien and therefore taxed only on US sourced in come.  Once a  US person ( citizen / GreenCard / Resident for Tax purposes ) he will be taxed on his world in come.   Note that on passing SPT, he is allowed to file a resident for the whole year.  However, because this will not be a 365 day year , he will not be able to use Standard deduction  -- must use the itemized deduction   which may be a disadvantage.

Is there more one of us can do for you ?

In closing I would say that TurboTax ( I am familiar ONLY with the desktop version ) is able to handle this situation.