In "The Game", Wesley was the only person trying to evade the ship's sensors and its crew, making it easy to identify the target as Wes by the process of elimination.
That's precisely my point. Even if they are only able to detect him by his "heat signature" and, for the sake or argument, no other identifying information is possible, under the new general orders, the computer would still have seen Wesley's humanoid-shaped body heat moving away from his discarded commbadge.
So when they ask the computer "where the fuck is the boy," and of course the computer already knows "the boy" means Wesley by inductive reasoning since when they're angry and referring to "the boy" it always means Wesley, is also able to know that the heat signature formerly assigned to the Wesley combadge is the present location it would be appropriate to report.
The only situations where Starfleet officers seem to take off their combadges are:
1. Trying to evade sensors due to naughty activities,
2. Trying to evade sensors because malevolent entities have posessed their bodies,
3. There is a high-ranking member of the Klingon High Council who needs murdering, or
4. They need to use it to generate a signal to beam something up or away.
In any case, it's a useful order and I refuse to accept that internal sensors wouldn't be capable of doing it.