This party would be a "single-issue party".
A single issue party is a political party who focuses on a single particular issue throughout its campaign. Historically, single-issue parties have not been successful in winning the presidential seat. However, some tend to thrive in a system based on voluntary voting, as all the voting base of people who support the party's position on this issue will probably vote during election day. The level of success of this political strategy depends on the relevance of the issue which is addressed. The higher the relevance, the more chances of success that the party might get.