So, I'll take a stab at this, although my son only committed verbally. His situation was a quid pro quo where he verbally committed and the coach agreed to help him with a very competitive admissions process. He did look at other schools that provided NLI after his verbal commitment.
The verbal and written commitment are worth the same...they are both a non-binding commitment. The NLI is a legal document and binding around financial terms. A few years ago I read the NLI terms and it was different from what I thought it would be... I highly encourage you to read it when you get a chance. Depending on the reputation of the coach and program, I think the written committment can be an extremely good thing or a bad thing with a false sense of security for the recruit. Personally, I like the idea of the written commitment so everything (terms, years, expectations) is put on a piece of paper and shared between the program and the player. College baseball recruiting is a complex marketplace with different processes and requirements across the different Divisions. I'd be curious why this specific program does this.
Good luck!