There's really no other choice for a bottom of the barrel build.
That's pretty much it right there.
G1610 is a solid CPU capable of solid things. It just won't be great at them. It's solid in most games, but falls flat on its face in certain ones. They sure are a nice price when on sale, though.
One thing about the nice gaming numbers the Pentiums and Celerons often put up is the benchmarks for those are only running the one thing. Add something as simple as playing a video on your second monitor while playing a game, and suddenly things can start stuttering a bit. Still playable, but not exactly smooth. Do something crazy like encode a video while playing a game, and the dual-cores without hyperthreading can feel some pain. But, what do you expect out of a low-end CPU.
I think if the friend is trying to put together a lower-end gaming PC, then a G1610 for the price is hard to beat, assuming the benches for DOTA2 look good to him. Like the OP said, if the friend wants more, he can always upgrade the CPU later. Ivy has only been "old" and "a dead socket" for three months.
One problem with Haswell is the boards are pricey compared to 1155. And if you want to go even cheaper and buy used, that's not a big market.
A used 1156 i5 is an interesting idea that was mentioned, but I haven't paid attention to those prices to have an opinion much more than "should be the cheapest way to get into an i5, uses about 25% more watts than Sandy."
A lot of the above goes out the window if you have a Microcenter nearby.