First of all Windows CURL requires to escape the quotes, from this:
curl -v --user username123:password456 --data-binary '{"jsonrpc":"1.0","id":"curltext","method":"getinfo","params":[]}' -H 'content-type:text/plain;' http://bitcoindServerIP:18332
To this:
curl -v --user username123:password456 --data "{\"id\":0, \"method\":\"getblockchaininfo\",\"params\":[]}" -H 'content-type:text/plain;' http://bitcoindServerIP:18332/
Also, in order to establish a connection for sending JSON-RPC commands from remote server I have enabled UDP port 18332 on that external server. Let me also remind you that bitcoind server is only listening to TCP port 18332.