There's nothing Greek or Roman about it. This is the traditional north Indian temple style, specifically Shiva temples. It's not particularly unique, there are plenty of north Indian temples in exactly the same style, specially among the Panch Kedar.

These temples were built at different dates, so there is no particular correlation other than they are temples to Shiva. What's different about Kedarnath is that it's unusually elaborate, which owes to its prominence as one of the "char dham" or four pilgrimage sites. The four traditionally were Badrinath, Dwarka, Puri and Rameshwaram but were expanded to include Kedarnath, Yamunotri and Gangotri.

The Kedarnath temple dates to somewhere between the 7th and 8th centuries, around the time of Adi Shankaracharya. It's hard to tell from that photograph, but those walls are 12 feet of solid stone. That's how it's survived in such an inhospitable climate up in the Himalayas.

I recall reading that the temple was buried under meters of snow during the little ice age for 400 years (1350's -1750's). The outside walls are scored with the marks of the glacier sliding by. Scientists carbon dated the lichens in the temple walls, and found a ~400 year gap in the lichen record corresponding to this period. More recently, it survived the massive floods and mudslides of 2013, when the entire town of Kedarnath was pretty much wiped out, but the temple still stands. Those stones are really massive.