You have correctly stated the consequences of the Blinded condition, and as you note, they do not result in a reduction in speed. A Blinded creature, including creatures without Darkvision in the dark, should be allowed to move without automatic movement penalties should they choose to do so.
Further, a Blinded creature should be able to hear and follow its quarry. The 5e assumption is that each creature knows the placement of all other creatures 'on the board' by both seeing and hearing them. In the absence of sight, or when facing an invisible foe, a creature still knows the location of other creatures 'to the square' by the sounds that they make. [Note that while this is not stated explicitly in the rules; it is a common, though not universal, interpretation] of what is in the rules.
Consider the complications in Chases
Other answers to this question, including the accepted answer, suggest using Dexterity or Dexterity (Acrobatics) checks for creatures moving at full speed while Blinded, and cite the suggested situations for those checks. I agree with this, but would like to add further rules support. The DMG section on Chases (pp. 252 - 255) are optional-but-official rules. Narratively, they posit a situation in which the action leaves a defined battlefield where the participants are moving at tactical speed, and enters unknown conditions through which the participants are moving at maximum speed. Doing so results in the sudden appearance of unforeseen 'complications', which are physical obstacles that must be negotiated to continue the chase. This, I think, is precisely the situation that would present itself to Blinded characters attempting to move at full speed through an unknown dungeon, as in your situation.
In the Chase rules, the complications that appear are randomly determined, likely because the DM does not have an appropriate map prepared; in your situation, you would introduce them at the points appropriate on the map (as you say, when there are stairs, narrow passages and a rickety bridge). Combining the two tables, we can see that the most frequent result is the character must make a skill check (usually Dexterity (Acrobatics) but there are others depending on the complication), with failure resulting in a certain amount of difficult terrain being applied. Other results of failed checks are being knocked prone, taking damage, or taking damage and difficult terrain. Certain complications call for saves (again usually Dexterity but there are others depending on the complication), with failure resulting in being knocked prone, taking damage, being attacked, having one's speed halved, being restrained, or taking damage and being knocked prone. I would suggest reading through the various complications and their consequences and finding the ones you think appropriate for a Blinded creature attempting to traverse your situations. As you state, these checks should be made at disadvantage if the nature of the complication would rely on sight to negotiate it.
Also consider Orientation
While the default in 5e is to assume that Blinded characters know the location of creatures on the board by the sounds they make, there is no such assumption for static environmental features. Instead, this part of the game falls under 'the DM describes the environment', and a Blinded character won't necessarily receive information about walls, doors, obstacles, etc. Should they run into these at full speed, treating them as chase complications would be appropriate.
Even in an environment relatively free of obstacles, if there are no sounds with which to orient themselves, it should be quite possible for a Blinded character moving at full speed to veer off course or otherwise get disoriented. In my games, I typically call for a Survival check for characters attempting to move at full speed when they can't see, with failure indicating they end up off course. This also allows me to fully describe the environment, or display a map, for the characters who can see, while the characters who can't see still have a chance to go off course without having to role play their ignorance of the environment.
A note on chasing goblins
Even those with Darkvision should have difficulty chasing down a goblin that knows the terrain, because of their Nimble Escape feature. A dashing speed of 60 is not great, but if is enough to get beyond the range of your darkvision, they can then Hide as a bonus action, either letting you run past them and doubling back, or confusing you whenever there is a decision point as you will no longer hear them and not know which way they took. On the off chance you are able to catch them base-to-base by dashing yourself, they get Disengage as their bonus action, meaning you won't even get opportunity attacks as you get deeper and deeper into territory that they know and you don't.