There's a difference between 'difficult' and 'defying player expectations.' This appears to be what's often considered a 'rage game,' and would probably attract a specific type of audience from most platformers, on its own. This makes it hard to speak for, on the matter of checkpoints - I've seen well-known titles in this niche, such as 'I Wanna Be The Guy,' which have save point. Nevertheless, how they're dispersed through the game presumably is based on differing design processes from standard platformers, so I'd recommend taking from similar titles, if you can't decide yourself. My opinion is that rage games do have to maintain some form of balance in this regard, at least, to ensure players who are into them don't actually ragequit.
For this instance in particular, I can't tell if they're bad at platformers, or if the controls suck somehow. Assuming the difficulty is sustained equally throughout, I could probably complete it no-checkpoint without too much trouble, if I really wanted to.