Some Muslim dynasties began through conquest, as many dynasties throughout Indian history did. But over centuries, Muslims integrated, intermarried, adopted local languages and customs, and became part of Indian society. Muslim-ruled states relied heavily on Hindu generals, officials, and allies, and their wars were largely fought over territory and power, not as some continuous occupation or religious war against Hindus.
Indian Islam is not a foreign invasion that destroyed. Indian Muslims are indigenous to India, and their ancestors converted for many reasons, including Sufi influence, social mobility, and escape from caste discrimination.
During the time that the British were looting India, the industrial revolution happened. That also helped India's economic decline, as does the fact that today, around half India's population are in agriculture, while contributing around 14% to the GDP.
The industrial revolution separated economic output from population size.