As long as the river crossing doesn’t take (significantly) longer than around 5-10 minutes, there’s probably enough air volume in that bag for CO2 levels (which are actually the more accute problem in an airtight space, not oxygen) to remain acceptably low
That bag probably has enough air volume to last someone around 5 minutes (give or take, probably give since that’s based on adult respiratory rates, and that’s a kid) before noticeable symptoms of hypercapnia (too much CO2, which will become a problem before oxygen deprivation does) start setting in.
Depending on how wide the river is, that’s not actually too much of an issue.
If there was an air outlet, the water pressure would force the air out of the bag. It’s clearly inflated at pressure in the image, proving it must be (mostly) airtight.
Classic republican. Doesn’t give a shit about a problem, until they’re personally affected by it.