The Jivatma will remain as a Preta unless Śrāddha is done, but non-Hindus do not perform Śrāddha.
Usana Smriti's Chapter 7 has the following verse:
It is laid down that Sapindikaran, S'raddha should be preceeded by the Daiva, (i.e., offerings made to the Deities). There one should invite the departed Manes and point out again (i.e., invoke) the deceased.* (17)
On this verse the translator/commentator (Manmatha Nath Dutta) says:
A deceased person is called Preta till the celebration of the Sapindikaran Shraddha , after which he is designated Pitri,
So, the answer to your question is a Yes, as per Hinduism (Hindu Scriptures). After death, the Jiva remains as a Preta till all the necessary rites are performed duly.
Sometimes, if persons had unnatural deaths, additional remedies are required to be performed for these souls to be relieved from the Pretahood and attain the Pitrihood.
Many of these remedies are mentioned in Satatapa Smriti's last Chapter:
For one dying of cholera one should treat a century of Brahmanas with sweet edibles. For one killed by fire sticking to the throat one should give away a dhenu of sesame. (48)
For one dying of a disease of the hair one should perform eight Krichchhas. According to this regulation one should perform the funeral rites for them. (49)
Thereupon being freed from the condition of a preta (dead) the gratified Pitris (departed manes) grant sons, grand-sons, longevity, health and wealth. (50) Here ends the [account of the] : fruits [of various] acts given by S'atatapa to his disciple S'arabhanga accosting him with humility, (51)
Therefore, according to Hinduism, anyone dead attains the Preta state. And, to relieve them from this Preta state, some rites are required to be performed, after which the Jivas are elevated to the Pitri state.
(NOTE:- This answer is from the perspective of Hindu scriptures. What happens to the non-followers of Hindu scriptures after their death is something that we shouldn't be concerned about on this site. We can't know that either unless we have knowledge about their rites and scriptures)
In this context, the below sloka from the Bhagavad Gita 2.27 is relevant -
जातस्य हि ध्रुवो मृत्युर्ध्रुवं जन्म मृतस्य च। तस्मादपरिहार्येऽर्थे न त्वं शोचितुमर्हसि।।2.27।।
For those who are born, death is certain. For those who die, (re-)birth is certain. Therefore you should not feel grief for what is inevitable.
(The only exception to the above birth-death cycle is for those who attain moksha, as Krishna himself says elsewhere in the Bhagavad Gita.)
English Translation of Abhinavgupta's Sanskrit Commentary By Dr. S. Sankaranarayan
2.27 Jatasya etc. Destruction comes after birth, and after the destruction comes birth. Thus, this series of birth-and-death is like a circle. Hence to what extent is this to be lamented for ?
Non-Hindus are certainly not an exception to the above rule. After their death, their rebirth is a certainty (assuming they have not attained moksha). There is thus no scope for any jIvAtmA - Hindu or non-Hindu, to remain as preta after death.
Do all Non-Hindus remain as Pretas after death?
No. Any Jiva is eligible to become sapinda provided the Jiva has enough merit.
The Jivatma will remain as a Preta unless Śrāddha is done
Although this statement is true to some extent, it is not entirely true. It is not the Sraddha alone that terminates the preta state; it is the Bhavana of Jiva that helps release its Pretha form.
The man having the desire of receiving the mess settled in his heart, and thinking it to be offered to him; is surely benefitted by its offering. (The funeral cake like every other food, is said to nourish the spirit, and cause its resuscitation in a new life and body). Whatever is in the heart and mind, the same notions form the nature of living beings; and whether these are in their corporeal or incorporeal states, they think themselves as such beings and no other. (The sense of personal identity accompanies the soul everywhere). The thought of having received the pinda cake, makes a man sapinda, though it is not actually offered to him; so on the other hand the thought of not being served with the cake, makes a sapinda become a nispinda (or one served with it becomes as one without it).
So, how does the Jiva in the Pretha state gets such Bhavana? The invoking of Bhavana is not in the control of the Jiva at that time; it is invoked automatically based on the vasanas (impressions) of the jiva.
Know this for certain, that no thought ever rises in any one without some cause or other; hence the desire or thought which is inherent in the spirit, is the sole cause of its regeneration on earth. Nobody has ever seen or heard of any event, occurring without its proper cause; except the being of the Supreme Being, which is the causeless cause of all beings, from their state of not-being into being. The desire is inherent in the intellect, like a dream in the soul; and the same appears in the form of acts, as the Will of God is manifested in his works of creation.
But, it is essential to note that Sraddha is mandatory to do as it surely helps the departed Jiva get such Bhavana as we are not aware of the state of the Jiva after death. As I mentioned earlier, even if we do Shradda, it will not help in terminating the preta state if the Jiva has wrong impressions (durvasanas)
A desire is naturally raised in one at its proper time and place, and by application of appropriate acts and means; and the rising of the desire necessarily overcomes its absence. Gloss. So a Sradh done in proper season and manner, serves to the benefit of the desertless spirit. The pious gifts made on behalf of the departed souls, accrue to them as their own acts; and the sense which they thus acquire of their worthiness, fills them with better hopes and desires of their future state. (Hence rises the hope of redemption by means of the redeeming son of man). And as the stronger man gains the better of his adversary, so the later acts of piety drive away the former impiety from the spirit. Therefore the constant practice of pious acts is strictly enjoined in the Sastras.
Hence, although performing Sraddha is essential for family members, it has to be viewed as an effort from their side for departed Jiva's well-being. It does not ensure the release of Jiva from Preta state. Not doing the Sraddha does not stop the Jiva from releasing from Pretha state.