I've tried to avoid too much Xmas shopping this year, and as a result I have a very short list of Xmas gifts for the chess player in your family.
For someone just starting out "Playing Chess: Step by Step" by Gary Lane might be a sensible purchase. One reason I am recommending it is that I cam across it bundled up with a glass chess set and board at my local shopping mall, and I suspect it is possibly available at a number of discount book operations that pop up around this time of year.
If you can track them down, a couple of old-ish chess movies might make a nice gift. Both "Searching for Bobby Fischer" and "Luzhin's Defence" come highly recommended, while "Black and White like Day and Night" could establish your 'art house' cred.
As for boards I'm certainly not suggesting the dead mouse chess set. I have seen a 'pop up' chess set in a couple of shops (DIY cardboard I'm guessing) while the old standby of the shot glass set might still appeal.
And finally, if you really want to give someone a surprise, but useful gift, entering them into the Doeberl Cup without their knowledge might just be it. Given how disorganised chess players are, this may be the only way they get to play!