Short answer: yes.
Related info in previous Q&As:
What kind of wood dust is toxic/dangerous and requires usage of dust mask?
Can wood dust cause irritation to other people in the house?
Do I need to worry about wood dust for very small-scale manual sanding?
It's not just wood dust you're dealing with here either, since there's sure to be dust from the paint or other finishes applied to the wood and a little glue from the construction of the doors. In actual fact they may be much more of a health worry than the wood particles that form the bulk of the dust, particularly as it's an old house — there could well be some remaining lead paint o_O
Vacuuming does not seem to get rid of all the sawdust on the couch, bed, comforters, in computers (!) etc., etc.
You just need to be persistent and thorough, and empty the vacuum cleaner regularly. You will eventually get it all, just as everyone who has ever cleaned up after building work eventually does get rid of all the dust. It just takes way longer than you're initially expecting because you have to do everywhere more than once. Three times seems to be the magic number in my experience. Consider yourself lucky it's not plaster dust which is much finer (DAMHIK).
Point to bear in mind is that dust is only an issue if you're touching it or, particularly, if you're inhaling it. If there's dust remaining in crevices around the home where it isn't easily disturbed to become airborne then you really don't have to worry about it any longer.
Re. the dust in the computer specifically, this isn't a direct risk to you since it will pretty much stay there. However, it is a potential fire hazard, at the least it may fry the computer without causing a fire that would spread so you should make a point of cleaning them (more on this below).
Unrelated to the woodworking side of things but I want to say something about it and the Comments don't allow enough space.
I was a rental tenant for many years and I'm sure your 'landlord', the leasing company, will have violated the lease agreement by letting someone in without your prior consent. The agreement might even specify that you needed prior notice in writing a certain amount of time before the work needed to be done (to give you time to tidy, lock up valuables etc.). Never mind that it was just some random bod hired outside HD which just makes it worse!!
Disappointed that they gave the keys to someone who started sanding and sawing a bunch of sticky and jammed doors without covering up the furniture beforehand.
"Disappointed" wouldn't begin to cover how I'd feel about it :-) I would be fuming if this happened to me and I wouldn't be shy about telling them so on the phone, or in person if necessary to get the point across. They gave an unvetted stranger access to your home, say it like that if you're not getting any traction.
Many people will tell you you should get the place professionally cleaned and present them with the bill. Ditto a bill for cleaning the computer, which you can do yourself (many guides online to explain and show you how) but may prefer to get done by a pro so you don't risk damaging it, or voiding your warranty.
If you wanted to, you may even be within your rights to break the lease and leave early (without penalty) over this, but local regs and the lease agreement you signed will determine that. Note that the former may take precedence over the latter, it does over here.