First of all, your statement is false, BITS Pilani is certainly ranked by the QS World University Rankings. BITS Pilani Overall ranking by QS World University is 1001 out of 1400 colleges in International in 2023 and it was 1001 out of 5500 colleges in International in 2021.
International rankings are a repetitive process, each year taking a fresh look at institutions that deserve to be included and institutions that deserve to be displaced. Usually, Indian universities struggle in international rankings because they are extremely teaching-focused, and thus their research is either lesser in volume, international recognition and influence, or both.
Over the past few years, top private institutions in India have brought changes in this system and are becoming more qualified for inclusion in international rankings.