some things in life are just easier to buy rather than make.... this may be one of them and I say may depending. However that being said I would personally have one major issue with this and that would be how to clean it. I hated most sippy toddler cups for the same reason, while cute pictures and name brands you would think they would think of the parent cleaning the cup especially if it rolled under the sofa or got left in the van over the weekend in the middle of the summer. But noooooo most are almost impossible to get totally clean without a toothbrush and tools used to clean cake decorating tips and denture cleaning tablets. Maybe that was just me being paranoid until I found the silicone topped ones that were easier to clean.
But how would you clean this out properly? The spigot and inside spigot, the container itself? I guess that's why boxed wines are so popular, they are disposable.
You said your friend was a wine lover, does that included boxed wines or just the ones in the bottles? Personally I'm NOT a fan of boxed wines including most bottled wines as I am not a fan of the vinegar taste and like sweeter fruity wines.
If you needed to make a bag that could be reused, and while a waste buy a box a boxed wine, dump the wine or use it as cooking wine and recycle the box and bag inside. Carefully open the box and maybe add some velcro to the closure so it could be opened and closed with ease and multiple times. You could spray paint the box if you wanted to make it a little nicer. Maybe use a base of kiltz to cover the print on the box first or just paint it black. Sew a bag to fit around the box which would give you a stable base for the bag and wouldn't flop over. Then sew the bag using stiff pellon stuff, the kind used for baseball hat bills and such. Add a layer of softness with a layer of polar fleece or iron on fleece to the inside between the outer and inner fabric. I have made cosmetic bags with both and it worked out nicely. Then use your button hole option as someone else suggested to make the hole for the spigot to pop in and out of. Don't forget to add the stiffening pellon to your handles. You could make the handles longer because if your going to the beach you might be carrying other things and you could pop this bag on your shoulder leaving your hands/arms free for other stuff to carry.
Another thought would be to buy a plastic container with a spigot such as ones sold for water to put into the fridge. They come in several sizes, are rectangle and make your bag to fit this instead. It would be heavier with the plastic, but you could also refill it as well.
A bag would be simple to sew, just cut 8 pieces of fabric the right size, (a quilting ruler and cutting mat rotary cutter makes this super simple to cut them the same) adding seam allowances and a little extra so it's not a tight fit. And fit one inside the other, use double fold bias tape to cover your raw edges at the top and add on your handles. It's super simple. There are lots of video's on youtube as well. Adding your pellon and fleece if you wanted to add a bit of softeness to the wrong side of each fabric. Practice your button holes with scraps with the pellon added so you don't muck up on the real thing. It doesn't need to be any harder than that. I have made lots of bags this way, various bags for my kids and halloween trick or treat bag just using two layers of cotton for those though.... If you wanted two fabrics for the outside so the bottom of the bag was different than the top, just cut them the way you want, and sew before sewing your sides together. Easy peasy, simple straight stitching.
Another thought is to make a round bag to fit say a liter or two liter bottle of soda. Recycle and reuse an empty bottle and pour the wine into the old pop bottle. You could even remove the label off a bottle and print your own fun label to put on the new bottle of wine. Personalizing it would be fun, and still legal at the beach because it's in plastic. If you cover the printed label with clear contact paper it will last a lot longer if your careful about washing it. (denture tablets would work dandy here since it has a small opening) Then once back home pour the wine back into the glass bottle it came in and wash out the plastic bottle right away and put it away for your next beach trip.
Just a few more ideas.....
Good Luck and I hope you post picts of what you come up with!