Minecraft – How to teleport only people within a specific area

If you only want to teleport people who are in a certain group, you can use the new scoreboard command to create a 'group' of people (using teams), and then teleport only that team with this command (targets nearest player in the group specified)

/tp @p[team=<internal group name>,<other params here>] <x> <y> <z>

To set up your groups, you can create a group like this:

/scoreboard teams add <internal group name> <display name>

And then add people to this group like this:

/scoreboard teams join <internal group name> <user name>

The advantage of this system is also that you can use it actually to separate groups in the actual game. The scoreboard command has a feature that means that the display name of a team will be displayed before the actual username, appearing like this in the chat:

[<display name>] <user name>: ...

More info on this system can be found in the wiki page linked above.

Changing the @p in the first command above to a player name will stop it from working, because parameters that are inside the [ and ] will only work for @p, @a, and @r. So you cannot substitute the first command above to /tp <player name>[r=2] <x> <y> <z>. It just won't work.
If you really want to use the r parameter on a single person, try using the above method that uses teams, but only put one person in the team. Here is a quick way to do this. Type these into the command console:

/scoreboard teams add <internal player name> <external player name>
/scoreboard teams join <internal player name> <player name>

And then in the command block, to teleport that person if they are in a radius of 2, you could use:

/tp @p[team=<internal player name>,r=2] <x> <y> <z>

Alternatively, you could just specify the name of the player in the selector. Following the previous example, if you want to teleport a certain person if they are in a radius of 2, you could use:

/tp @p[name=<player name>,r=2] <x> <y> <z>

This was a very interesting challenge for me to work out. There are many parts to this problem, which are a lot harder to accomplish than one might think. There's identifying the player with the status effect, and identifying a set of random players who are not them (since /tp Unionhawk Unionhawk is a valid result of /tp @p @r, and does nothing).

But, finally, here is my setup, which works for a bounded number of players on a server. Some of its flaws include only allowing one game to be played on a given server, and using experience level to identify players. As such, /gamerule doMobLoot false must be used, and /gamerule commandBlockOutput false is strongly advised.

So there's quite a lot of things going on here, as you can see. But this is all accomplished using 4 commands and a hopper clock.

The Group 1 command blocks are there to detect when a player has the specified potion effect, remove it, and proceed to the matching Group 2 command block. I used /effect @p[c=n] 4 0 for that one, which removes the mining fatigue effect from player n on the server (going down the list of players on the server). When that command evaluates, the Group 2 command blocks give that player one level of experience using /xp 1L @p[c=n].

From there, the next time the hopper clock pulses, the "Group" 3 (you only need one) command block teleports a player with 1 level or more to a random player without any levels using /tp @p[lm=1] @r[l=0]. When this command evaluates, the "Group" 4 command block clears the experience level of all players using /xp -9999L @a.