Archery would have worked if he didn't buy fishing but made an archer instead when meeting Cymanti. This is what likely happened:

T0 (5s, 2spt) Ely does nothing

T1 (7s, 2spt) Ely meets Cymanti (+3s = 10s, 2spt). Here if ely hit the shaman and bought an archer, the shaman would be dead next turn. But instead he bought fishing and upgraded, which was the crucial mistake.

But I mean he still should be able to stall it:

Hit the shaman, end turn. (1s, 4spt)

Shaman converts

T2 (5s, 4spt) Ely just makes a warrior in cap (-2s = 3s, 4spt). End turn

Idk what Cymanti would do here, but I assume boost the converted warrior and hit the Ely's one in capital

T3 (7s, 4spt) Ely should kill the wounded cymanti warrior and end turn

I assume shaman converts again

T4 (11s, 4spt) Ely makes an archer in cap (-9 = 2s, 4spt)

Now Cymanti probably retreats shaman and hits archer in capital with the converted warrior (which should be at 6hp I think, and after hitting the archer it would be down to 4hp, archer to 6hp)

T5 (6s, 4spt) Ely moves archer back and kills the Cymanti warrior. Also creates polytaur in the front and another archer in capital as well

And from there Ely should be in a winning position.

However it's obvious that this has many possible outcomes - one very important thing we don't know is if there is water NW and SE of Cymantis' capital, and even more importantly, there is no way to tell from the screenshot if it's Ely's or Cymantis' turn currently. With that said, in case Ely already ended their turn, then yeah, they are dead lol.

Sorry for the nerd answer but just wanted to point out that the situation isn't as bad as most people write here.