It's a pretty simple rack using two wood mounts and some elastic to hold it in place. He is not a hard core gun nut or anything crazy like that, just a practical person trying to protect his garden, farm, and beehives from critters.
The bike is a new addition. My brothers and sisters bought my parents two second hand bikes in December for Christmas presents. After not having bicycles on hand for twenty years my parents have embraced cycling again usually going for 5 to 10 mile outings once a week. Both are in their sixties, and my dad newly retired now uses the bike for lots of neighborhood commuting (ex. cycling to church, to the neighbors, to creek). Its pretty cool to see.
I looked around the web and found another DIY rifle carry for a bike. This guy just attached a backpack scabbard to his front basket.
There's even a commercial gun rack that mounts on the handlebar. Do you point the rifle toward or away from traffic?