Will the medium be able to last 100 years?

It's on actual film, not digital, according to this article:

The finished movie (which was shot on film and will require an old-school projector to exhibit) has been put in a bulletproof safe with a 100-year countdown timer, along with a bottle of Louis XIII.

Film can survive that long in a canister under good conditions, see for example the films of Mitchell and Kenyon from the turn of the 20th century which were found in 1994 and restored (available on DVD).

Early film used various cellulose derived plastics for the basic medium, these (especially cellulose nitrate, which can be used as an explosive) are inherently unstable and can break down very quickly in poor conditions.

However modern film stock is based on polyester which is a lot more stable and even under normal storage conditions should last 100 years without too much trouble.

Furthermore, if the film is locked in a sealed safe it should be a lot better protected than just keeping it on a shelf in a can. For example it could be filled with inert gas and oxygen/moisture scavenging materials. Indeed if these inert dry conditions can be maintained you can preserve many things well for a century.

Also just the fact of being in a safe will protect against ultraviolet radiation which is one of the main things which causes plastics to degrade. Plus being untouched for this time it shouldn't be subject to mechanical damage form handling etc.

For something like this analogue transparent film stock has the advantage that it is essentially a series of real images and so even if film projectors are entirely obsolete by the time it is opened the images will still be there to see and even if all knowledge of films projectors was lost it would still be fairly easy to scan and digitise the content as there is no need to reverse engineer digital codecs.

Really 100 years isn't that long to preserve anything if you set out to do it under controlled conditions. There are still plenty of original photographs from the first world war around and many of them weren't specially archived for a most of their life.

There are many media that would last long enough.

A metal "father" of the blu-ray version kept away from oxydation (e.g. in oil) can last basically forever, and produce as many new copies as you need after your 100 years.