Proper Water Heater Venting?

I inspected a house last week and it had a shorty gas water heater under the stairs. It looks like it has an attachment on top of the water heater to allow the exhaust to vent sideways (because of the stairs). The vent continues sideways through the drywall into a closet and then up and through the roof. But on the other side of the exhaust vent is another rectangular looking vent, and when the the water heater was heating I could feel heat escaping from this rectangular vent. I am suspicious about the venting but I’m unfamiliar with this type of hot water heater venting. Also the initial exhaust vent tube continues sideways and is at best perfectly level. Comments welcome.

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Check with your local AHJ about putting fuel-fired appliances under the stairs. It’s not allowed around here.