Do I need conduit for an indoor sub-panel feeder line?
A brief visit to the code indicates that there is a bigger problem, in that the ampacity of 8Ga copper is only 55 at 90C (aluminum 45 Amps) so your wire is too small for a 100 amp service. You need a bare minimum (if everything is rated for 90C) of 3Ga copper or 2Ga aluminum, and probably larger after various derating factors are applied, or if 75C is the limit on any connection. There is a note that may permit use of 4Ga copper for 100 amp in a dwelling unit as a "service lateral" - you'll have to decide how you feel about taking that note seriously. I've linked to a handy calculator that might be instructive.

Ampacity calculator for branch circuits and feeders

Non-pickily, for a wire appropriate to the ampacity of the subpanel, no. If you are using an 8-3 w/g cable, the cable is probably fine, and being a cable would complicate running it in conduit (as opposed to 4 individual wires.)

Pickily, maybe, if the wire is running through an area where it's prone to damage, or through a floor - but in both those cases, the conduit is only needed in the affected area, and is a "sleeve" rather than a "raceway" for code purposes.

If you don't already have the 8-3 w/g cable bought, do compare costs .vs. THHN or THWN (or XHHW, etc) in conduit. Edit: Well, even if you do have it bought, you can't feed 100 amps with it, so shop around for bigger wire.

I have a personal bias in favor of conduit, but that's all it is. I've seen too many scary things in remodeling where rodents have stripped NM cables in concealed spaces. In addition, you are limited to the 60C rating when using NM cable.