Here is what I got from Traffic Police officer:
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Thank you for your email
The two crossings shown in your photos is not a pedestrian crossing. As such, you would need to give way to motor vehicles before your cross. However, if a vehicle appear while you are crossing halfway, the vehicle should give way to you.
I hope that the above clarifies. Thank you.
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So, this means in Singapore, vehicles have right-of-way over pedestrians, unless pedestrian crossing. This is surprising, and very dangerous basic expectation. But it explains why cars trying to squeeze in on my way when I walk or when I run.
More vulnerable has right of way on the road is basic rule in other countries. Pedestrians has right over bicycles. Bicycles over cars... In Singapore, it is opposite. Car has right of way over pedestrian. Everybody, please be careful.