Maybe there's just nowhere easy to stow his walking stick, or he's anticipating using it some time soon.

I'm an ambulatory wheelchair user, which means that sometimes I use a wheelchair, sometimes a wheeled walker thing, and sometimes a walking stick. My wheelchair didn't have a convenient place to stow my walking stick until I made a dedicated holster thing for it. There is a pocket at the back of my wheelchair, and various places I could stuff my stick temporarily, but it would inevitably end up falling out, falling over, or getting stuck in the spokes of the wheels.

The particular walking stick this guy is using doesn't look like it folds up like some do, so the storage problem seems especially relevant. Basic sticks like that one do allow you to set it to minimum height, collapsing it down a bit, but that's a faff to get it set to the right height again for when you need it.

Maybe this guy is approaching a security checkpoint or something, where he'll be expected to stand up to go through a scanner (airports and the line are capable of handling people who can't stand up from their wheelchair, of course, but things often go faster and easier if you can bear to stand up for a few moments, in my experience). Or maybe he's heading to the bathroom — whilst an accessible bathroom would typically have grab rails and the like, the stick might help him to push himself into a suitable position to be able to grab the rails and transfer onto the toilet.

What's more, anyone who uses a wheelchair who has some level of walking ability is generally advised to do stand and walk as much as they're able to, to reduce the risk of muscle atrophy, blood clots, pressure sores etc.. Even without something that necessarily requires him to stand, he may be trying to make it easier.

Finally, I'd just like to add that I think that in scenarios like this, the best response is to just shrug and go "well, I don't understand why he'd do that, but I guess there must be a reason"; Although in this post, you have been as respectful and non-judgemental as you plausibly can be, I think questions like this are coming from a place that is a bit judgemental.

Part of my motivation for this last bit is my own experience with a similar kind of curiosity, and I'm someone who is disabled myself, and immersed enough in disability activism that I know tons of disabled people, who all manage their disabilities in such varied ways that I keep finding new instances of how a person manages their condition that surprises or confuses me. A lot of things don't make sense to me, but without having direct lived experience of that person's particular circumstances, it's not for me to say what makes sense or not (and disabled people spend so much time having to justify themselves and their needs that they shouldn't have to fit into neat little boxes, even if it's just in someone's head).

This is a long way of saying that ultimately, despite my speculation, I don't know why he's using the walking stick like that, and even if I could ask, it wouldn't be appropriate to. I really don't want to come across like I'm telling you off here, especially as it does seem like we're on the same page re: not being assholes to disabled people. I just wanted to try to add some nuance to how we think and speak about disability

Others have answered better and it's a joke , but as a general reminder (to put it in plain language and succinctly):

Not all disabled are always the same amount of disabled at all times.

(It gets old having to explain why a person is in a wheelchair one day, is walking with a cain one day, is bed ridden some other day. Life is complicated. Probably a good rule of thumb is to just let it go, unless you know them well enough to actually have a real conversation about it, and not just make passing comments that make them feel bad.)