This is actually the parser misunderstanding where the error is. It is actually complaining that it's trying to read the response_models and response_parameters as blocks instead of attributes. There's further discussion of this in the 0.12 documentation.

The main difference between a map attribute and a nested block is that a map attribute will usually have user-defined keys, like we see in the tags example above, while a nested block always has a fixed set of supported arguments defined by the resource type schema, which Terraform will validate.

In 0.11 you could interchangeably get away with using the block syntax (just curly braces such as response_parameters { ... }) for attributes but in 0.12 it is stricter around types so this is no longer possible. The code in the Medium post you linked to as a working example is 0.11 code and isn't valid in 0.12. If you look closely at the GitHub code you also linked you can see that it uses the attribute syntax instead of the block syntax so is valid.

Switching to using the attribute syntax by adding an = will make this work as expected:

resource "aws_api_gateway_method_response" "options_200" {
  rest_api_id = aws_api_gateway_rest_api.scout-approve-api-gateway.id
  resource_id = aws_api_gateway_resource.proxy.id
  http_method = aws_api_gateway_method.options_method.http_method
  status_code = "200"

  response_models = {
    "application/json" = "Empty"
  }

  response_parameters = {
    "method.response.header.Access-Control-Allow-Headers" = true,
    "method.response.header.Access-Control-Allow-Methods" = true,
    "method.response.header.Access-Control-Allow-Origin"  = true
  }

  depends_on = [aws_api_gateway_method.options_method]
}