1. The IAF wants planes fast (G2G order, ie no Make in India)
2. The IAF wants planes cheaper to operate than the MKI (hence the initial single-engine requirement)
3. The IAF wants planes cheaper to acquire than then Rafale (hence the existence of this program in the first place, otherwise they would have just ordered more Rafales)
I don't think this about the F-35 because the push was specifically to allow twins in the competition
What twin engine aircraft best suits the AF's goals AND would have pushed the GoI to change the rules in the first place?
Why the SH of course
From a GoI perspective, choosing SH for both IAF and the Navy keeps the overall fleet simpler, enhances engine commonality (LCA, SH and AMCA all using F414) and makes ordering carrier aircraft simpler. Instead of having to guess exactly how many carrier aircraft they'll need, they can just use the extra in the IAF. Then if greater naval needs arise, it's simple enough to transfer the planes over. Conversely in a situation that needs land-based aircraft, the SH is already integrated into the IAF infrastructure and it would be possible to shift a squadron from a carrier to an inland base.
The SH might be 'almost' as heavy as the MKI, but it's still substantially lighter and combined with less thirsty engines makes it quite a bit cheaper to operate.
The USN is working on another 3 year block-buy and upgrade programs continue apace. In fact the USN is doing another upgrade program for legacy Hornets, and if they're working on keeping those pieces of junk modern, you know the SH will be relevant for decades to come.
In terms of something that 'just works', is affordable, reliable, offers basing flexibility and is available quickly, it's hard to beat the SH.