The "Maratha", before the creation of their kingdom, were a group of Hindu aristocrats with greater wealth and power in their region than average citizens. They were not kshatriyas, unlike the northern Rajputs, but rather "made" kshatriyas through a dealing between Maratha Emperor Shivaji Raje Bhosale and a brahmin.
The Maratha always relied on the success of their light cavalry. Their speed made them far superior in their geography of their homeland against Mughal invasions.
They were rather inspirational to other Hindus in the region, which helped in their efforts to conquer the entirely Islamic kingdoms around them. This was aided by a religious tolerance greater than that of most Muslim kingdoms and a confederate government that allowed local rulers with presence in their regions to govern independently. These attributes allowed them to make and keep massive gains in territory through a relatively short period of time.
For their specific regions of control, they never held all of Carnatica, but the regions in the game map are not flexible enough to give them a substitute. On the campaign map, the regions which they would control circa 1730 are Bijapur, Ahmadnagar, Malwa, Berar, Gujarat, and perhaps parts of Hyderabad (which was actually its own state).
By the zenith of Maratha power (circa 1760), it would control Rajputana, Orissa, half of Hindustan, and border portions of Bengal, Sindh, and Punjab. Mysore was never conquered. Cochin, Goa, and the rest of Carnatica were also never conquered.
While cavalry was extremely important to Maratha victory, melee infantry was still more common in terms of numbers by 1700. The Maratha did not use the bow to a great extent; the spear/lance was known to be used as a javelin, though. Cavalrymen (and possibly some infantry) would charge with them, toss them at the enemy, and fight with swords.
After an alliance with the Rajput states, the Maratha did employ Rajputs to help them fight. However, the alliance was relatively short as it was destroyed during the Third Battle of Panipat (1761), along with a good portion of the old Maratha veterans. Most lost territory was regained, but the Peshwa's prestige was damaged by the loss. Afterwards, British conquests of neighboring territories would eventually rise to conquests of the Maratha themselves. The Anglo-Maratha wars would chip off Maratha territory and eventually consume it all. Most of these conflicts were instigated by the Peshwa's submission to the British for succession rights, angering the Maratha chieftains.
They also never conquered the entire Mughal Empire, much less the entirety of India.
Surprisingly, they did make peace with the Mughals in 1719 and officially ended their war in return for a 35% tribute of revenues in Mughal provinces in the Deccan to the Maratha. In return, the Maratha officially would accept Mughal rule in the Deccan and pay tributes.
This part is somewhat confusing to me as the author continues that the next Peshwa, Balaji Rao I, would conquer more Mughal territories right after 1720. I'm assuming the Maratha simply took the one-time revenue cessions and broke the treaty. By 1940, Rajasthan, Delhi, Orissa, and Bengal were already reached. (I still assert my point that this is far from Wangrin's claim that the Maratha defended Maharashtra from 1700-1760)
Also worth mentioning; while many units like Sikhs did not find themselves in Maratha service, since many regions in the map were not conquered by the Maratha, one could simply say that they would recruit them in a what-if scenario.