This question seems to be doing two things:
- asking for confirmation that fire is required
- and, based on the assumption that it is, asking if ocean vents could fill that requirement
This answers purpose is to point out that fire, (or high general heat), MAY NOT BE REQUIRED for development of technology in an aquatic environment. AND I am providing a different solution.
First: NO it appears fire is NOT required for technological advancement.
I am recycling another answer to a similar question to explain: this question*.
*(as in I am almost completely quoting the answer I added to that question).
However it provides an alternative to the requirement of needing fire to smelt metals... it would require the race to
- experiment a lot,
- possibly find solvents for metals (heat from vents may help here)
- and likely methods of isolating the desired metals
...I suspect it would be possible for a bioelectric race, to learn advanced forms of electroplating & electroforming.
My limited understanding of electroplating is:
Dissolve a metal
Develop a 'mandrel' in the desired shape
Utilize an electric current which, in some way, bonds the metal to the mandrel (not exactly sure on the details of how...)
All of the above steps seem likely to be possible & even possibly easier, in an aquatic environment.
Electroforming is actually even more interesting, in that it is used to create highly detailed as well as much thicker products.
Electroforming could be used to actually produce things such as knives, swords, etc... out of metal, (not just a coating of metal on something else more easily formed).
Additionally electroforming can be VERY accurate in reproducing highly detailed forms/mandrels, even, if I understand correctly, on the nano scale (the scale of the transistors our current computer chips are measured in).
This would very much support the idea of making computer circuits in a similar form as our PCBs (Printed Circuit Boards)... to go with your other post on that topic (and what got you thinking about this one).
Hopefully the above is helpful for you when developing your race.
I highly recommend reading this answer from Culyx on this very topic.