This is a terrible design for someone who needs assistance getting up and down stairs, may just break their neck if it fails. Thin strips of wood (MDF no less!!) on a compressible padded carpeted incline is a very weak link, along with the poor assumption that the little side pieces will last.
There are other issues like needing a rail on the wall since it does not have a method of preventing swaying backwards, that it doesn't clear the top of the stairwell so an accident there would mean tumbling that much further down the stairs, and that if (when) it fails, there is nobody to sue while in some areas of the world, a person's insurance would cover much of the cost of a lift professionally designed and installed, by a company with insurance and liability.
I'm all for DIY gadgets but not in this case unless much better engineered than that. The first place I'd start is metal L-channels instead of wood, anchored down every meter or so. You could do better using U-channels set sideways so the wheels can't come out, and put a seat belt on the seat. Yes that would cost more, but those MDF rails are a joke. I haven't gone into the durability of the cheapest winch you can find either, considering # of times a person would use this is probably a minimum of twice a day which adds up over years.
What happens if the winch fails, does it become a roller coaster? Seems like a solenoid actuated brake stop that is deactivated going down and with a manual engagement switch would be a good idea since there is no testing to see how long before it breaks and what happens then. Maybe put a phone at the base of the stairs too so when someone tumbles down the stairs they can call for help if not paralyzed.
If you are frail enough to not be able to go up and down stairs, the solution should at least be less frail than you are!