Claiming a trademark is distinct from registering a trademark. You can claim a trademark by just saying "this is our trademark." That will typically be done with the "TM" symbol. Registering a trademark means you applied with the USPTO to get a registered trademark, and it was granted.
You are correct in that they don't make an explicit claim, but I'm not sure if trademark law actually requires you to do that. It would certainly make everything less messy.
> I'm not sure if trademark law actually requires you to do that.
It definitely does not. It certainly could influence a court decision (there's always a degree of uncertainty with any court case), but you absolutely can defend a mark that you have not explicitly claimed or registered, as long as you can demonstrate sufficiently widespread prior use.
You are correct in that they don't make an explicit claim, but I'm not sure if trademark law actually requires you to do that. It would certainly make everything less messy.