'other-oriented' is a Modern English compound formed from 'other' + 'oriented'; 'other' ultimately comes from Old English 'oþer' meaning 'another/other', and 'oriented' comes from the verb 'orient', derived from Latin 'oriens'/'orient-' meaning 'rising (of the sun)' which developed into senses of 'to set toward' or 'to align'.

The element 'orient' entered English via Latin 'oriēns' (present participle of 'orīrī', 'to rise') and Old French 'orienter' meaning 'to turn toward the east' or 'to align'; in English 'orient' and its participial/adjectival forms ('oriented', 'orientated') acquired the figurative sense 'directed toward' or 'focused on', allowing compounds like 'other-oriented' to mean 'directed toward others'. 'Other' comes from Old English 'oþer' and developed into Modern English 'other'.

Originally 'orient' referred to the rising of the sun/the east; over time the sense shifted to 'set or align toward a reference point' and then figuratively to 'direct attention toward', so 'oriented' came to mean 'directed toward', and 'other-oriented' now means 'directed toward others' (concerned with others).