Bundled game giveaway...is possible?

Well even if this isn't a referral link, I'm not sure if you are allowed to do this or not.
If you check the bottom of this page, you'll see that there is a 3 days suspension for advertising (although oddly this isn't mentioned in the guidelines. Maybe something in the Terms of Service ?).
So it depends if they see this as advertising or not. I suggest you clear things with the staff before doing this (you can create a ticket in the Other category for that.)

But come on, these are just free keys you hoarded... if you want to promote your channel, at least buy a bundle for it

So have you contacted support yet?

You can. I leave a random video that usually links to a song I like in most of my giveaway without issue. The part where you can get banned for advertising is if you just made a thread that just linked and nothing else. If you make a giveaway and asked nicely (i.e. not make it a requirement to watch said video but an option), you will be fine. There is a guy who makes daily giveaways here already just for the sole purpose of promoting his channel: here.

You can. There are quite few people doing that already. As long as it's more along the lines of "if you have spare time, feel free to check out my channel > insert link" and not "Pls subscribe for more giveaways"

I sell paintings online and I asked the mods about promoting my stuff when I first started using the site. I was told it is fine to post links in giveaways as long as they aren't referral links and you don't actually require anyone to do anything (such as 'like' a facebook page) to enter a giveaway.

In any event I certainly see plenty of other people linking youtube videos in giveaway descriptions without getting suspended.