Can I enter Spain with a Ukrainian passport traveling from a non-EU country?

According to the link you provide, residents of countries like Ukraine may use that exemption to enter Spain only if

siempre que procedan directamente de ellos, hayan transitado exclusivamente por otros países incluidos en la lista o hayan realizado únicamente tránsitos internacionales en aeropuertos situados en países que no constan en el anexo.

Or, in English:

provided that they come directly from them, have transited exclusively through other countries included in the list or have carried out only international transits in airports located in countries that do not appear in the annex.

(Spanish government translation at the link above)

As you would not be coming directly from Ukraine, you would not qualify for this exemption.

As of this writing, there is a separate exemption for travelers who "dispone de un certificado de haber sido vacunado con una vacuna autorizada y con una pauta completa administrada hace más de 14 días" (in English according to the government translation, "have a certificate of being fully vaccinated with an EMA/OMS authorized vaccine, and the last dose was administered more than 14 days ago.")

Apparently the fine rules for this exemption are still being developed, so you may wish to do more research if you believe you qualify for it.