Free CloudFlare protection covers it...?

Hello.
I own a VPS which hosts a main domain with 4 sub-domans, 2 of which are for a TeamSpeak3 and a gaming server. Now, I know it might sound like a completely noob or silly question, and I know CloudFlare free protection plan covers any DDoS attack towards your website. But, can I use it to protect my gaming server and TeamSpeak3 server from DDoS attacks too? Or this type of service works only with websites?
Finally, what the cheapest plan to have an anti-DDoS service that works for my websites and both my servers?
Thanks.

https://community.cloudflare.com/search?q=teamspeak

What do you mean? I can simply add the game server’s and TS3’s sub-domains in the control panel and they will be DDoS protected?