There aren't any particular terms for a "backpack friendly" camera other than portable. With hiking, space and weight are always the two primary factors, so it's up to the user to decide what is worth carrying. Some will cart a full DSLR and big optics for the performance they give and others will use their cellphone because it is already with them and has a "good enough" camera.
As for the idea that AA/AAA batteries are a better way to go than rechargeable batteries for the camera, you couldn't be further from correct. The weight and size to power ratio of most rechargeable batteries is FAR better than that of conventional AA/AAAs. I get significantly more power out of two LP-E6 batteries for my Canon 5D Mark iii than I get from 6 AAs and the two LP-E6 batteries are both smaller and lighter. It is more expensive to get enough of them to cover multiple days of shooting, but at around 4000 exposures for two of them, having even 4 is enough for a pretty significant amount of use. (Granted, a 5D mark iii is on the heavier side for hiking, but the same principals apply for smaller cameras.)
In terms of best quality for the size and weight, it's one of the few times that mirrorless can really shine. They have very light weight bodies and while not quite as capable as a DSLR, they can support solid quality optics. They aren't as rugged as professional grade DSLRs though, so if they are going to take abuse, a good ruggedized point and shoot may also be a decent option. Bringing a full DSLR may still be worth the weight though if you want the maximum quality.
You can also look into alternate power sources such as solar or there are even hydrogen fuel cell options that can provide sufficient power for most electronics and have an even better weight to power ratio for longer trips.
Update: seeing that this is for a friend rather than for yourself, the best option that will be cheaply available is probably to look for a cheap viewfinder camera if you can find one that will allow them to take photos without needing to use the screen. The screen is the biggest power drain on any camera that requires their use and most point and shoots require it for framing a shot. A viewfinder camera gives the general idea without needing to use the screen by approximating what the shot will look like, but tend to have a fairly basic feature set as the viewfinder doesn't look through the lens and thus can't zoom. The upside to that is that it means that the optics can be fairly simple and most of the money likely goes in to the sensor. It makes the camera a little less versatile, but probably increases quality of images (for the price) and durability (fewer moving parts).
