Yes. Most nationalities apply online these days. But I think tourist and business visas are still not being given due to the pandemic (it is still closed to the world.)
Before it had to be done at the embassy and yes or yes you needed to be a valid DNI holding Argentine resident to apply here. For business visas I remember there being requirements like showing your bank statements, letter of invitation, pay-slips etc. Took about a week and there was an option for a rush visa. Tourism is much easier and probably quicker I understand.