The stargate is the principal travel mechanism and one of the most significant elements of the show. There is a great amount of pressure on the developers to get the stargate right. Firstly the stargate itself will be featured in many more design locations than they had the ability to do so in show. This may include different ramps and stairs, and different mounting mechanisms.
In the television series the stargate can be opened for a maximum of 38 minutes (or more in special circumstances) and when the last traveler steps through the gate always knows when to shut down. This would create problems in a game situation, particularly on heavily populated worlds.
A number of solutions to this have been discussed, including instancing the gate area. However the most likely mechanic will be that the gate functions as expected on unpopulated worlds. The user will dial the gate and watch the dialing sequence and kawoosh occur, the team then steps through and the gate cuts off. It has been largely discussed on the official forums, whether the wormhole animation will be used as a loading sequence or not, and so far it has not been confirmed. It might not be possible due to limitations on the Unreal 3 engine. Its still a matter in flux.
On populated planets when the gate is already open, players will be able to come and go as they please without having to go through the dialing sequence. The gates are not connected as a game programming, so the other end will not see the gate being activated, at least not the opening sequence.
Exactly how this will work, particularly with the iris and related mechanisms, and which worlds this will include has not been revealed. The gate mechanism will likely be one of the items fine-tuned during the beta phase.
Of course when the gate function is an integral part of a location or quest it should function as expected. Not all places have active stargates and you may need to get to the planet by other means.