I think you're looking at this at the wrong angle. This is a great way to learn composition and remixing and all of that stuff -- but you're sort of looking at it from a 'what do I need to change' angle, as opposed to, how can I take what I've learnt here and write a new peice inspired by these ideas? I think you should start getting into that habbit - of doing these things as excersises, then completely going off and writing your own piece in the style of, or inspired by that music, but not thinking about taking the progressions and everything with you. Copyright technicalities aside, it will just leave you frustrated and in a bit of trouble IMO.
You said Rythms and chords cannot be copyrighted right? Well the only part that sounds similar is the beginning, which is essentially just a rhythm.
That's a very general/blanket way to look at it. By themselves, sure, you can't copyright a chord or a rhythm but it's more about the context they're used in than the individual subjects.
Sure, many pop songs share our good old friend the I IV VI V progression or something similar, but the treatment and context is often pretty different, and even when it's not, that's a pretty understood, generic progression these days that usually is surrounded by enough difference to be seperate things. Like a standard 4/4 rock beat. It's a device, that obviously can't be copyrighted - but it's used within a different context.
In your case you've got a lot further than just 'using the same rhythms', the first track sounds dangerously similar to the example you posted -- you'd surely have to call that a remix and give credit...I don't consider yours to be a completely different track at all. You have to be careful saying 'it's just a rhythm', when it's a distinctive one that uses the exact same sort of synth sound then you're running into trouble, especially when using a lot of the same harmonic material. You're not just copying the rhythm in this peice.