If I were designing such a thing with the current endpoints, I'd wait for a user to request:
1. Latest game list, or
2. Analysis of a particular game.
Unless you really want/need your analysis to be available before someone asks, that would only hit api.chess.com when some data is wanted.
You don't say in any detail what type of analysis you intend to do, but:
1. chess.com offer in-browser analysis (via Stockfish.js) which is near-instant but more limited for free members
2. Download of any game which can then be fed to an engine.
If you're doing something like #1, chess.com has chosen that as one of their encouragements for people to move up to premium membership.
I'm developing software that needs to access a user's most recently completed game. I see that I can get the games in near realtime using e.g. :
https://api.chess.com/pub/player/ck_russ/games/2019/02
But this something I probably want to poll every 10 seconds or so potentially from numerous players since users may want to also use the software on games played by their friends or favorite players. As each archive grab could easily grow to thousands of games it seems like this would be a drain on both chess.com's resources, as well as that of my users. Is there any other more efficient way to obtain recent completed games?
If there isn't I'd propose an API endpoint along the lines of: api.chess.com/pub/player/ck_russ/games/after/TIMESTAMP which just returns the 0 or more games played and completed after TIMESTAMP.