Doubt that the new concrete path is sufficiently angled to drain nearly all rainwater into the large brown metal grid drain next to the two steps.

Some rainwater running down the new concrete path (or dribbling down the brick side wall) will likely still drain into the 3mm wide cavity (see final three pictures below) beneath the nearby existing brick side wall located shortly before the two stairs.

In essence, rainwater hitting the brick wall above the 1.8m section of old concrete path will drain into the 3mm wide cavity evident in final three pictures herein.

We wont know until we receive a major downfall.

Application of a waterproof membrane (available at Bunnings and easy to apply) would -

a)    fill the below evident three 3mm (ave) cavity between old concrete section of path (2m long) and existing brick side wall; and

b)    be applied to about 30mm up the wall and about 20mm onto the old concrete.

Back in 2009, when Phil Johnston held an Owner Builder Permit from NSW Dept of Fair Trading, he applied a Crommelin waterproof membrane over the upper slab of a new large double garage that he had constructed.  The waterproof membrane comprised a solution that resembled think paint and dry powder cement mixed together. 

Thick rectangular floor tiles were then applied to the top of my new double garage by a seasoned floor tiler.

As concrete expands a little in hot weather, the waterproof membrane would need to be slightly flexible.  Bunnings would likely provide a slightly gel product to combat the concrete movement between summer and winter.

In summary, application of a waterproof membrane (costing under $100) to the 2m long x 3mm wide opening (evident in the final three pictures) might mitigate rain water leaking under Unit 1 that might, or might not, be a concern.

Water evident in above two pictures seems to have come from an overflow pipe and does not to deviate twds the old metal drain.

Below three pictures evidence leaves that have slipped into the old cavity between the side wall and the old concrete path.  Cavity appears about 3mm wide in parts.