While identification with religion maybe a truism, caste as such, does not play much importance, unless one is standing for election or if one is from a historically underprivileged class, which is given quotas for education, jobs or promotion as an incentive for emancipation for the last 60+ years.
The religious and regional distinctiveness of Indians cannot be understood by foreigners, let alone a Chinese. India is actually very diverse and while there is a whole lot of commonality, but the distinctions can also is very pronounced. The Chinese cannot understand because the Chinese historically have removed the distinction through 'assimilation' and therefore, all Chinese claim to be of one class, even though there are distinct difference amongst them, including customs, cuisine and language or dialect, if you will.
Sikhism and Hinduism is unique in its way. The religious distinction sort of blurs and yet is distinct. A contradiction it appears, but it is not. Hindus visit Sikh Shrines and pray with the same revernce as they would in a Hindu temple and vice versa.
Therefore, while the Singapore Army Chief maybe by ethnicity an Indian, yet his being a Sikh is a distinction that cannot be overlooked for historical reason, if any. The Sikhs were in the vanguard in the maintaining of separate identity of the Hindus during the Mogul period.