I'm aware of notes crossing clefs, but I've never seen it being used like this before. For the record, the song is in 4/4.
There's two things going on here that may be a bit confusing.
- There are cross-stave notes, like you already noted.
- The rhythm is a so called 'tresillo' rhythm, that's often used in latin-american music. Here the rhythm is structured as 3+3+2 in eighth notes. The note groupings and accents reflect this rhythm. That's why it can seem a bit awkward to read when you approach it as a 4/4 rhythm, but using the groupings like this is actually the clearest way to notate this.
It can take a while to get into this kind of 'groove' but after a while it's very pleasant and dance like to play. It's also interesting to note that on all accents there is a left hand chord.
One thing to add to Tim's excellent answer: Notice the first three eighth-notes in the measure are written in a way that implies two hands should be used (one in each staff). The remainder of the measure, the final 5 eighth-notes, are a bit ambiguous, and quite possibly spaced too far apart to be playable with one hand, but are certainly a single phrase. There's an implicit set of rests for the lower hand which are not written into the lower staff. AFAIK that's common notational style for piano scores.