The imp has 3 d4-sized hit dice and can spend them during a short rest like any other creature can.
As explored in the questions "Where are a monster’s hit dice found in the stat block?" and "How do creatures spend Hit Dice after a short rest (if they can do so)?", a monster's hit dice can be determined from the dice expression used in ...
D&D 5e uses the natural language meaning of words, unless contradicted by a defined game term. Benefit is not a defined game term.
Benefit, under the normal meaning of the word is:
an advantage or profit gained from something.
Being able to change spells is contingent on completing a long rest.
The Rakshasa's curse reads:
The magical curse ...
Rules As Written (RAW): Maybe
There is some ambiguity due to the word "benefit" not being used in the Resting or Class sections of the PHB, and that has an argument for being consistent between both.
Contrasting this are several magic items that regain charges after a long rest (most state dawn though). There is also a subclass (I forgot which, so ...
Is it a benefit? Yes. It's certainly beneficial to be able to change spells, in that it lets you get access to spells you didn't previously have prepared, with no real downside, since it's optional.
Does it result from finishing a long rest? Yes, the rule for changing prepared spells says you may do it upon finishing a long rest, but doesn't say you can ...
From the preparing and casting spells section for the cleric:
You can change your list of prepared Spells when you finish a Long Rest. Preparing a new list of Cleric Spells requires time spent in prayer and meditation: at least 1 minute per Spell Level for each spell on your list.
Note the word "finish". You don't prepare spells during a long ...