The short, non-useful answer is fairly simple - they can if the game is designed in such a way to allow them to work.
All real-life small-unit tactics are based on a handful of very simple principles - namely, achieve a larger volume of fire than your enemy in order to allow your own men freedom to maneuver and ultimately destroy the enemy.
The problem of course, comes in the concept of volume of fire and maneuver. In a game like gears of war for example, it takes an enormous quantity of fire to bring down a single opponent and as such, simple volume of fire is not terribly effective in the general sense. Yet even in this game you find that while volume is not terribly important, relative lethality is and as such, any time you outnumber your opposition (the only way in the game to achieve any kind of fire superiority if player skill is equal) you will find that the odds of compleating any sort of maneuver increase dramatically.
Most FPS games however favor neither volume of fire or maneuver - instead they rely almost entirely on the careful application of fire by individual players. Modern Warfare (or the sequel for that matter), a game that seems like a prime candidate for the application of the most general prinicples of small unit combat, has a combination of mechanics where most game modes are actually openly hostile to any attempt to apply real life tactics. While lethality is certainly present (and as such volume of fire becomes important), the freedom of maneuver becomes almost entirely irrelevent. Distances in the game are so short and cover so ineffective that it is rare any gun battle lasts more than a few seconds. Assuming a target(s) could be suppressed, sending other players to flank is almost certainly a wasted effort. In the time it takes for the unit to maneuver, the fight is almost certainly over. Worse still, the most commonly played game modes result in a constantly shifting battlespace who's only real tactical features are areas of varying inherent danger when attempting to transverse them. If you consider that only a handful of the game modes offer players a compelling reason to stand their ground and fight, you realize that the game most people play most of the time has very little in common with scenarios in which real life tactics were developed. Having proper lethality matters little when there is little freedom of or incentive to maneuver.
Oddly, while the most general principles rarely make their way into games, a different (but related) set of tactics can and in fact often is applied to games like Battlefield - that is the principle of combined arms. As any player who has spent much time with the series will attest, any attack tends to be more successful when players properly coordinate the available assets. When a single tank (or even small group) attacks a stronghold, the result is usually a few casualties on the defending team and an enormous pile of wreckage for the attackers. If a pure infantry assault is attempted, the result is generally a bit more successful but often gives the same result. Yet, somehow, when combined an infantry/tank assault tends to be more successful than the sum of it's parts might imply. The reason is relatively simple - the biggest danger the tanks face is anti-armor weapons - the infantry accompanying the tanks are ideally suited to destroying such annoyances. The biggest danger facing the infantry is machine gunners and riflemen from the defenders - a problem that the tanks are ideally suited to face. When properly applied, a combined arms offensive allows an assaulting (or defending) force to minimize their weaknesses and as such maximize their offensive potential.
Of course, such things are rarely well coordinated and few games actually allow for a true combined arms approach. Often, it is simply by sheer luck that such a tactic is attempted - a great enough quantity of players descend on a point and haul with them their preferred (or smiply available) assets. Such a move generally succeeds, both because of the strength of the combined arms approach to combat and because when it occurs it is usually the result of a significant portion of a team being in the same spot.
Of course, everyone uses some variety of tactic when they play an FPS game, unless they simply act at random and hope for the best. In your average game of battlefield for example, you'll find that most players naturally seem to hold a basic understanding of a few principles. Snipers for example, generally understand that they need to try and occupy a vantage that has wide sight lines and preferably overlooks an avenue that enemy infantry are likely to cross while players who favor armor tend to understand that they need to use their tank at the points of greatest resistance for maximum effect. Without any real coordination however, the inevitable result is games are won and lost primarily because one team either has significantly more skill on average or simply because the particular collection of players on one side just happen to prefer tactics that support one another. A well coordinated team can often be far more effective than a highly skilled group of individuals. To put it in perspective, while snipers might be useful in certain moments in a game of battlefield bad company, if you have been pushed all the way to the final point, chances are quite excellent that you would better serve your team using a weapon that favors close quarters combat over one that favors long ranged precision.