Do engines calculate using "brute force"?
No.
Searching fast does not mean using "brute force". It's like a person who calculates much faster than everyone else: they certainly aren't counting on their fingers one by one (and even if they wore their fingers out, they couldn't keep up).
Mainstream CPU engines all use alpha-beta (ab) pruning search, which prunes an enormous number of branches during the search. A strong engine has a branching factor below 2. That means when the search reaches a position and goes one level deeper, it examines fewer than 2 moves on average and prunes dozens of others.
GPU engines (using the search algorithm of AlphaGo) use a generalized MCTS, designed to work with neural networks of complex architecture. Their search speed is far slower than that of CPU engines, so it is even less likely to be "brute force".