Your question is overly broad and liable to be closed as such, but I'll bite:
The documentation for the SDK is available here: https://developer.sony.com/develop/wearables/smarteyeglass-sdk/api-overview/ - it describes itself as being based on Android's. The content of the wearable display is defined in a "card" (an Android UI concept: https://developer.android.com/training/material/lists-cards.html ) and the software runs locally on the glasses.
Things like subtitles for prerecorded and pre-scripted live performances could be stored using file formats like .srt ( http://www.matroska.org/technical/specs/subtitles/srt.html ) which are easy to work with and already have a large ecosystem around them, such as freely available tools to create them and software libraries to read them.
Building such a system seems simple then: each performance has an .srt file stored on a webserver somewhere. The user selects the performance somehow, and you'd write software which reads the .srt file and displays text on the Card based on the current timecode through until the end of the script.
...this approach has the advantage of keeping server-side requirements to a minimum (just a static webserver will do).
If you have more complex requirements, such as live transcribing, support for interruptions and unscripted events then you'd have to write a custom server which sends "live" subtitles to the glasses, presumably over TCP, this would drain the device's battery life as the Wi-Fi radio would be active for much longer. An alternative might be to consider Bluetooth, but I don't know how you'd build a system that can handle 100+ simultaneous long-range Bluetooth connections.
A compromise is to use .srt files, but have the glasses poll the server every 30 seconds or so to check for any unscripted events. How you handle this is up to you.
(As an aside, this looks like a fun project - please contact me if you're looking to hire someone to build it :D)
