Praise be to Allah.
Do note that Allah has commanded the worshipper to beautify and adorn himself for prayer, as He says (interpretation of the meaning):
“O Children of Adam! Take your adornment (by wearing your clean clothes) while praying”
Adorning oneself for prayer is something that is additional to covering the ‘awrah. Hence women are commanded to cover their heads when praying, although they are allowed to uncover their heads in front of their mahrams.
Shaykh al-Islam Ibn Taymiyah said:
With regard to adorning oneself for prayer, it is something that is additional to covering the ‘awrah, and it is based on the Qur’aan, the Sunnah and scholarly consensus. In the Qur’aan, there is the verse (interpretation of the meaning): “O Children of Adam! Take your adornment (by wearing your clean clothes) while praying” [al-A’raaf 7:31], which Allaah revealed because the mushrikeen used to circumambulate the Ka’bah naked. Every place of prostration is a mosque (masjid), and this indicates that covering oneself for prayer and tawaaf is what is meant by adorning oneself to worship Allaah. Hence the word adornment is used rather than the word covering, to demonstrate that what is meant is that a person should adorn himself and not limit it to simply covering.
Once this is understood, although the worshipper must adorn himself for prayer, this adornment may vary from one country to another, according to their customs, including what is mentioned in the question, which is praying in a garment with half-sleeves. If the custom of that land is that the best adornment is to cover the head or to pray in a garment with full sleeves, then praying when one is dressed as mentioned in the question is contrary to what Allaah has enjoined, even if the prayer itself is valid. But if the custom of the people in that country is to dress as described in the question, then there is nothing wrong with praying dressed in this manner.
It should be noted that the ruling also varies according to variations in the dress itself. The garment may have short sleeves and that may be customarily worn in some countries where it may be worn as an adornment, or a man may go to work in it and so on. In that case there is nothing wrong with praying in it. Or it may be the custom that this is not a kind of adornment, and it is something that a man wears at home only, or when sleeping only, in which case it is not appropriate to pray in it.
And Allah knows the best