There are several long-range archery clubs nearby, including:
https://malvernarchers.com/
If that's a possibility, does that mean the man and dog were in a restricted area? Would there not have been warning signs posted that this area was in an active archery range?
I've done a bit of archery in the dim-and-distant, most archery clubs shoot at targets a few tens of metres away in a farmer's field, sports field or some other piece of open land where the owner has given their permission. There's usually a very clear view around and beyond the targets. Arrows that miss don't usually fly
too far.
My brother-in-law does clout archery, where archers shoot at a flag up to approx. 200 yards/ 185 metres away; landing within 12" / 3.5m scores points. (He's proud of his longbow, but will happily regale you with his knowledge of Tudor archers who practiced with bows of such high poundage they developed skeletal abnormalities, discovered when the remains of Henry VIII's warship
Mary Rose- including bowmen and their weapons- were retrieved in 1982).
Obviously this requires a greater consideration of safety, and clout shoots are normally well-planned events on private property.
Hunting
anything with bows is illegal in the UK, I guess the authorities finally decided to get even with Robin Hood. Field archery, where the archer proceeds through e.g. woodland to engage different targets is a sort of substitute but not as popular as traditional target archery. Like clout archery, normally conducted in an area where access can be controlled and with the landowner's permission.
Arrows can flex a little, but the object in the footage looks too curved (and appears to lack flights, normally brightly-coloured to aid retrieval).
(Just to get some kudos from the bro-in-law: Arrows are loosed or released, maybe shot, never "fired"- no fire is involved. Since the invention of firearms we've become used to using "fired" as a description of anything propelled at speed towards a target, but archers disdain this

).