I love that rug too. I'd go for it. If the patterns don't match up, you can always return them to the store (even if it's an online purchase). I'm wondering about the canvas backing though. That might make it slippery? Maybe you want to have it professionally installed with a pad? I wonder if a pro would remove the canvas first. My stair runner was installed with staples and a pad. No stair rods. The savings on on not having to buy rods might cover a good portion of the cost to install professionally. There's another link to that rug pattern where you can see more of the design. Here is a link that might be useful: Linden Street Wool Rug

Any good carpet installer would be able to do it. Should be no more than $500.00. For reference, we typically pay around $250.00 for the stairs when they are installing the remaining portion of the house.

I had mine bound, not sure what serged would look like

Don't know if your parents have any low vision issues as they age but if they do, be cognizant of that when you select a runner or stair treads. Advice from the American Academy of Ophthalmology: Stairs. Changes in the floor surface are one of the greatest fears of the visually impaired. Stairs should have a handrail, be well illuminated, and have minimal glare. Put a contrasting strip on the leading edge of each step; without that, the stairs can look like a ramp to a person with low vision. Stair treads naturally create a leading edge (nosing) as that part of the step is exposed and contrasts with the tread when using a tread that doesn't blend with the stair color. Certain patterned rugs e.g. horizontal or vertical stripes, obliterate the effect of a leading edge and make stairs very dangerous even for those without low vision. You may also want to consider some kind of wireless motion sensor stair lighting. Lots of options out there.