You're referring to the railway signaling block system. Comparable systems exist for airports, with taxiway blocks managed by a central application, relying on taxiway centerline (TCL) lights progressive activation. In such application clearances and paths are all digitalized and use by the application, in addition of being transmitted by voice. Such application can exchange data with aircraft avionics.
Aircraft and vehicles are located using cooperative systems ADS-B, SSR, multilateration, ground sensors and radars. Compared to railway blocks, the airport system is more complex, vehicles can form queues, velocities must be managed, size may determine invalid paths and clearances, etc.
Two aircraft taxiing to the same runway, one is restricted, the taxiway centerline is prevented to illuminate in green past some limit:
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These applications are based on specifications agreed at ICAO level, and known as Advanced-Surface Movement Guidance and Control System (A-SMGCS) Services, described in Doc 9830. The specifications have four levels of increasing complexity.
For the case you cite: Conflicting clearances between a departing aircraft and a taxiing aircraft, this would be shown like this:
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This case is part of Airport Safety Support Service specifications:
The Airport Safety Support Service provides an automated alerting service to Controllers. It detects and triggers at least one of the following types of alert: RMCA, Conflicting ATC Clearances (CATC) and Conformance Monitoring Alerts for Controllers (CMAC). The Airport Safety Support Service is using the Surveillance Service, the Routing Service and the input of electronic Clearances.
There is an existing question: What is the Surface Management (SMAN) all about? answered by @DeltaLima, citing the application SMAN as implementing these specification (levels 3/4).
Such applications, which are part of ATC safety nets, are already deployed on some large airports:
Generalization to large airports is in progress, e.g. in Europe within SESAR initiative. Deployment may be progressive, e.g. implementing levels 1/2, then 3/4, because hardware is required both in ATC premises and on the airport surfaces, this has a cost.
You can see a demo video here related to how stop bars are managed. A workstation at Riga airport (Latvia):
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Examples of critical alerts
ROUTE DEVIATION A mobile deviates from its cleared route on a taxiway (close to an active runway).
STATIONARY An arriving aircraft or mobile crossing a runway has stopped within the RPA and
does not move within a certain time period.
NO TAKE-OFF CLEARANCE An aircraft is cleared to Line-Up and it takes-off without a Take-Off Clearance.
NO LANDING CLEARANCE An aircraft is close to the runway without a Landing Clearance.
LANDING ON THE WRONG RUNWAY An arriving aircraft is detected to be aligned to a runway that differs to the assigned runway.
RED STOP BAR CROSSED A mobile crosses a RED stop bar (Intermediate Holding Point or AoR
boundary).
LINING-UP ON THE WRONG RUNWAY A departing aircraft is detected lining up on a runway that differs to the assigned runway.
RUNWAY INCURSION A mobile is detected entering, or predicted to enter, the RPA without a Land / Line-Up / Take-Off / Cross / Enter Clearance.
RUNWAY TYPE An aircraft is on a runway that is not suitable for the aircraft type.
TAXIWAY TYPE An aircraft is on a taxiway that is not suitable for the aircraft type.
RUNWAY CLOSED An aircraft has entered a closed runway.
TAXIWAY CLOSED An aircraft has entered a closed taxiway.
RESTRICTED AREA INCURSION An unauthorised mobile is detected entering, or predicted to enter, a restricted area.
HIGH SPEED An aircraft taxies with speed exceeding y knots (y=parameter).
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