Ah yes, the New Year's Purchased Stone gate. It's pretty much gone at this point in time, but for future reference for anyone who sees this and intends to pull out Next Year's Grab Bag Gate on... next year:
That specific gate requires you to actually buy stones. That's what the "Note: Requires 50 Purchased Transient Stones" are for. Of course, if you don't buy stones, you can't summon through that gate, period. In that case you'll have to use other summon gates instead.
Stones in this game are divided by two types:
"Purchased Stones" (stones you bought in-game, not including the bonuses you'd get from buying lots at once)
"Free Stones" (every other stone you get in the game aside from buying stones, including bonus stones you get when buying stones)
e.g. Let's say you bought the 175 stones (103 counts as Purchased Stones and you get 72 Free Stones as a bonus). Meaning you can pull from that gate twice, because you have 103 Purchased Stones. And IIRC, apparently you can only pull from it once, so you'll be spending 50 Purchased Stones regardless, getting 1 guaranteed 5*. However, WHICH 5* you'll get isn't guaranteed, so you might end up still getting a "meh" one.
Understandably, that part of the stone mechanic sucks. Unfortunately, it's not the good or great kind of suck you'd expect from this game's myriads of husbandos.
It's very tempting to get guarantees of pulling out the rarest of them all though, I'll give it that at least.