From brief and rather humorous text of WTFPL license it seems like I can just take the code, slap GPLv3+ sticker on top of it and live happily ever after. Is this really so? Am I missing something? What if somebody else takes the same code and use it in proprietary product?
Yes you could do that. GPLv3+ is much more restrictive than a WTFPL license so if someone else had an interest in the WTFPL license code you copied they would be much more likely to use it instead of the GPLv3+ re-licensed code you create.
WTFPL is meant to be freely used by anyone (almost public domain). Your best defense is to make important substantial changes to your re-licensed GPLv3+ code so that a copycat using the original WTFPL code will be not be able to use all of your improvements
Can I just take the code and slap a GPLv3+ sticker on top of it?
This is covered in the WTFPL FAQ:
Q: Can’t you change the wording? It’s inappropriate / childish / not corporate-compliant.
A: The WTFPL lets you relicense the work under any other license.
So yes, Word of God says you can do that.
What if somebody else takes the same code and use it in proprietary product?
Nothing. The WTFPL does not transfer copyright. The copyright stays with the original author, who gave both of you a non-exclusive permission to "DO WHAT THE FUCK YOU WANT TO" with their code. You can't violate each others copyright because none of you owns it in the first place. Both of you are just using it under permission of the original author.