I’m with @Clarity that the phrase refers only to two things—longing and aversion (in some form)—not to all five hindrances.
The phrase abhijjhādomanassā also occurs in descriptions of sense restraint, as a part of right effort. For example in AN4.14 (my translation):
Since you could be overcome by bad, unwholesome qualities of longing and aversion if you left the sense of sight unrestrained, you practice restraint over it, you protect it, you undertake its restraint.
By restraining the senses, you reduce your mental reactions towards experience, whether reactions of attraction or repulsion. Sense restraint doesn’t really affect all hindrances directly, such as doubt or sleepiness. (In a way it does, but that is clearly not intended in the above statement.)
Now, right effort leads to right mindfulness (e.g. AN10.121). So when you have right mindfulness, you have abandoned these two things (abhijjhā & domanassa) completely. That abandonment is what vineyya loke abhijjhādomanassā I think refers to. And in this context abhijjhādomanassā refers particularly to the coarser forms of the first two hindrances: sense desire and ill will.
Also, in the standard description of right mindfulness, the phrase is loke abhijjhādomanassā. The world (loke) seems to me quite clearly to refer to the world “out there”, the sensual world. And while it makes sense to abandon longing and aversion with regard to this world (loke), I don’t know what it would really mean to abandon sleepiness or doubt with regard to it…
So these hindrances don’t seem to be part of abhijjhādomanassā.
Consider also texts like SN35.247:
And how are you restrained? Then, when you see sights with the sense of sight, you do not get attracted to (adhimuccati) pleasant ones or become averse (byāpajjati) to unpleasant ones. You are non-forgetful [or mindful] about the body.
While the words here are different, I think they reflect abhijjhā and domanassā. The passage reflects the practice of right effort (particularly sense restraint) leading to right mindfulness.
I agree vineyya means “having removed”. That’s another reason abhijjhādomanassā can’t refer to all five hindrances, because the removal of the five hindrances is the purpose of right mindfulness, not it’s prerequisite. (See e.g. AN9.64)
So I agree with the sutta commentaries (relying on to Piya Tan) that abhijjhādomanassā refers to (the courser aspects of) the first two hindrances, especially longing and aversion regarding the sensual world. It includes the kind of emotions and thoughts that distract you from being able to keep a single thing in mind, to have some basic form of mindfulness. In the scheme of the eightfold path, the job of abandoning those kinds of emotions and thoughts is that of right effort, not so much right mindfulness.