Liquid, along with Solid Snake (And possibly Solidus) were born in 1972. TPP takes place in 1984. As far as I can tell, this "Eli" looks like a 12 year old boy. Not to mention, the slicked back blonde hair, the resemblance to Big Boss, the fact that he "curses his fate" (Recalling to Liquid's hatred of his genes in MGS1, him thinking that genes are his fate, etc).
No doubt about it, this boy called Eli is Liquid Snake.