Am I missing something, or is this a WTF?
The guy has lived there for years, reports no clogs, no issues.
No real purpose for it unless they have had back-up problem(s) in the past and this was offered as a solution. Since it is atypical I would mention it in the report even if a problem was not suspected.
Was this the only one in the home? How close to the main sewer drain connection point was it?
Is there a washing machine near the sink?
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Is this sink located on a lower level? A clogged main will spill at the lowest fixture. However, that check valve isn’t allowed to be there.
Is that a NY thing?
There are no restrictions to placing a swing check valve on a lavatory or sink unless it would reduce the drain line diameter. If you use the Building Codes one would be required if the fixture flood level rim is below a specific point in the sewage system.
These valves are typically rated not to reduce the pipe discharge size (sized for that) but we would not known unless we have the valve manufacturer information.
What is questionable is the connection on the downstream side (don’t know material types of the line at the wall) and I would have expected anyhow some type of compression fitting so it can be removed for maintenance/repair if needed.
In any case it is atypical and suspect and to use a variant of a Marine’s phrase “Write em all up and let the Plumber’s sort it out!”.
My WAG - Maybe thay removed the check valve and it’s now the access point to feed the snake in to clear out the forever clogging drain lines.? 
This is on the 1st occupied floor of 20 unit apartment building, above a parking level. Building 1960’s construction of slab concrete — other words they can’t alter the plumbing. No other unit had a swing check valve. The central laundry was at least 100 feet away at the main vertical stack.
The building had for the era the typical evidence of snaking activity, but nothing extreme **
My concern with the swing check valve is potential for clogging, and near certainty that with no disposal the swing operation will be blocked by food debris or grease eventually. This particular resident reported the sink has worked fine for his three years.
** for this era building I can tell how frequently drain clogs by looking in the tubs. Bonus points for anyone who can figure out what I’m looking for.
Yep, likely history of backing up. Old cast-iron likely having some problems. Since it is the lowest apartment, slow drains backed into this unit. Now it will just back up into the stack and slowly recede. Recommend a sewer scope.
Reasonable concern IMO and should be reported on. As well as the visible corrosion at the connection.
Also notable.
Galvanized.
Possible insufficient slope (through the parking level) to reach the central stack.
All concrete building (including interior walls).
I see galvanized there in your photo, not sure what the remaining drain, waste, and vent system is. In my area cast-iron is prominent. Regardless, this pipe is considered at or past its expected useful life.
Maybe, could be one of many issues. IMO, a scope would reveal not only the pipe material but it’s condition as well as slope problems, offsets etc. Something I always recommend with materials of this age.
Brian hit on the key points and why I was curious as well.
Yes clogging is a concern even with a disposal as particles can attach and block the valve. Again nothing prevents it but it is atypical, a good find, and I would certainly report on it.
As for what you are looking for signs of back-ups I would and do look at the overflow drain port for debris since they are seldom exercised and debris can easily remain, also waste sitting for short periods can leave a nasty looking ring(s) (depending on height and number of times) around the tub that might be difficult to clean off.
Older tubs have cross bars or a strainer built in. If the tub has never been snaked, it will be intact. I can tell which buildings have regular plumbing calls, because most of the units will have ragged torn metal, where the plumbers just made their snake fit.
Every drain is intact? Probably a problem free building.