Disclaimer: not a quant but I've built a similar system.
>some low latency twitter API that you can pay big money to access
Yes. The twitter firehose is the big one, where you get a stream of _all_ tweets. Twitter doesn't publish the price, and one source claims $360k/y for half of the hose. https://econsultancy.com/want-your-own-twitter-firehose-you-...
>And then I guess that goes to some array of GPUs to run the NLP model as quickly as possible?
General speaking, trained models usually aren't so big that you need a cluster of GPUs, or even a single one. Sometimes running it on a CPU makes more sense because if it's small enough it's just easier and cheaper.
In particular, basic NLP and sentiment analysis is pretty easy, especially like in this case when you're dealing with a very limited vocabulary. A free CPU based library like https://github.com/cjhutto/vaderSentiment should be good enough.
> And the NLP results get traded on by placing orders with an exchange?
Yes. Doing this quickly is pretty tricky, but financial institutions like JPMorgan Chase would have access to an extremely fast and low cost (per trade) API to do this. And then they probably already have the tech to strategically place big orders, so the other bots don't realise what you're doing. Or just use a private exchange, aka a dark pool: https://en.wikipedia.org/wiki/Dark_pool