I would say it depends on the rest of your outifit/your general 'style'. But I don't think you are too 'old' for that backpack. Looks absolutely fine and stylish to me.
I should say tho that I am late 50s, and have a VERY casual 'style'. (And that I LOVE backpacks!)
I always wear a small backpack when I go out, and hardly ever bother with a hand bag unless going somewhere 'smart'. But I don't work, & don't generally/often need to worry about how I look. (Or what other people think.)
I have a black/grey backpack for everyday use/light shopping. It's a "Hedgren" fabric one which I bought years ago. (Still going strong.)
It's a bit like this one, but not exactly the same. www.hedgrenwebshop.com/hedgren-great-adventure/maledives-m-backpack-black)
And then I have a 'proper' (bigger) "outdoors rucksack" for heavy duty shopping, for actual "hikes" & for airline travel when I'm travelling in 'casual' mode. (Cos I can get my laptop and lots of books etc in the bigger one.)
IMO, it's MUCH better for your back/posture to use a small rucksack, (than a shoulder/hand bag), and less likely to get stolen by an opportunist thief. And I just love having both my hands/arms free for other things.
I usually also use a waist-bag for my money/any small valuables, as more secure in front. (And again it's hands-free.)
I am never without my backpack, and I LOVE it, but I probably do look a bit like I'm on a post-retirement gap year most of the time?! 
HTH