You have 2 problems here:
1 - potential for CO buildup
2 - condensation damage to the building
1 - gas driers may or may not have a seperate vent for the combustion gases. However, they would usually route the combustion gas outside. It *may* be acceptable to vent the combustion gases indoors if there is *guaranteed* minimum ventilation in the vicinity of the drier and the room is of a specified minimum size (e.g. it's OK for a gas range to vent its combustion gases indoors - but there are strict building codes on minimum ventilation and size of room, etc.)
There are 2 ways in which you can get CO build-up. You can get it from a malfunctioning or badly set-up gas burner (even very minor maladjustment can produce dangerous CO levels). However, you can also get it if there is inadequate ventilation; there have been cases of fatal CO poisoning caused by people blocking up permanent ventilation grilles in a room with a furnace or other gas burner.
If there is any reluctnace to do anything by the landlord - get a CO detector immediately (you should be able to buy one from any local supermarket today - round here CO detector stickers are about $5. Just stick it on the wall. If CO is detected the sticker changes from pink to black permanently), and install it in the laundry room.
2 - this is really the landlord's problem, as the moisture and condensation will wreck his building. However, he may claim that damage due to mold and condensation may be, at least partially, attribuatble to you not opening windows/doors, etc. In which case, you've got an awkard situation over who pays for the damage.
Quite apart from damage - you will also end up with bigger energy bills, because the clothes won't dry in a hot humid environment.
Write to the landlord - tell him you don't think that the dryer is safe because of CO/condensation issues - and that you cannot use it. The lease includes the use of a dryer, which you currently don't have, and you are therefore deducting $25 a month from the rent until it is fixed, or until he gives written confirmation that it is safe (in particular safe from CO buildup), and that you will not be liable for any damage caused by excessive condensation/mold.
In the very unlikely event that he does write to you telling you it is safe, I still wouldn't take his word for it. However, you would have cast iron proof of gross negligance that you could present to a local buildings inspector.