The article skips over the board entirely, but Travis must have been blindsided by his co-founder Garret Camp and early CEO Ryan Graves for this to have transpired. The board likely threatened to fire him unless he resigned, because there's no way Travis walks away because of this investor letter. It's more than likely the letter just provided the air cover his old friends needed to send him packing.
edit: For those replying that Travis has control of the board, please cite your sources. Being the majority shareholder using dual-class stock is a much different thing. Shareholders elect board members, but you can't remove investors' board seats, that language is boilerplate in financing documents.
Uber does not need the backing of the investors from the letter to remain solvent. With the exception of Fidelity, these aren't big players. Hundreds would take their place immediately given the chance.