The rule as written does not in any way restrict the size of the creature that is to be climbed on. So, it would seem that any creature that is:
- Larger than you by at least one size category (as indicated by the title "Climb onto a BIGGER Creature")
- Of a size that you can grapple
you may use grapple to traverse the creature.
if the creature is:
- "Sufficiently large" (DM discretion)
- You cannot grapple it because of its size
then your DM may rule that you may use terrain rules to traverse the monster.
Seeing as this is a general rule with no contradicting specific rule, I think it is very fair to just take it at face value and say that any creature meeting the above two requirements are able to be climbed.
If one creature wants to jump onto another creature, it can do so by grappling.
This is unambiguous. To climb onto the back of a larger creature you need to use a grapple. Thus, this must follow the grappling rules.
A Small or Medium creature has little chance of making a successful grapple against a Huge or Gargantuan creature, however, unless magic has granted the grappler supernatural might.
Again, multiple explicit call-outs to grappling which is clearly what we are mechanically doing here. Using a grapple to climb onto a larger creature's back. Additionally, it says that you can't grapple a creature more than two sizes bigger than you (restating the grappling rules).
As an alternative, a suitably large opponent can be treated as terrain for the purpose of jumping onto its back or clinging to a limb.
This phrase is referring to the previous paragraph. As in, "As an alternative to using grapple to climb a larger creature...". It is saying that if the creature is sufficiently large (left up to the DM it seems to decide what qualifies) then, instead of grappling (because you literally can't grapple them), you can treat the very big creature as terrain.
To climb a creature, use a grapple if it is a size larger than you that you can grapple. If its bigger than you can grapple, your DM must decide if its sufficiently large enough for you to treat it as terrain.