Words like "race", "biracial" and "multi-racial" are imperfect descriptors, but are currently the most familiar and/or convenient when trying to identify certain groups of people. "Ethnic", "bi-ethnic" and "multi-ethnic" are more accurate, I think. I use both sets of terms interchangeably.
"Race" is an imperfect and tricky term that does have some scientific and social validity:
Ethnic ancestry, and the geographical regions that correlate with various ethnic groups, can be traced by way of ancestral genetic science, for the discovery of cultural and political traditions associated with those particular ancestries. Also, some ethnic/racial groups are demonstratively more prone to suffering from certain diseases, relative to other ethnic groups. ... So race (ethnicity) does have a biological basis.
Mis-guided interpretations of "race" can cause problems, like when someone who has DNA results showing s/he's about equally East Asian and European, calls himself (just) Asian, because his phenotype (appearance) is more Asian, and society has placed pressure on him to only consider himself Asian because of that pressure.
Or maybe that same man wasn't pressured into a singular Asian ID, but just happens to connect more with Asian culture. When describing his ethnicity, instead of saying, "I'm Asian and European, but identify more with Asian culture," he just says, "I'm Asian", opting to answer sentimentally, instead of giving an accurate reply.
Some folks lean on the "race is just a construct" meme to avoid a discussion about racial politics or discrimination. They figure: deny race exists and I won't have to discuss it. It's not unlike pretending we all live in a "post-racial" world.
Some mono-racial folks will say that "race is just a construct" when they want to deny someone's biracial or multi-racial identity. Ironically, they're still willing to place themselves into a singular racial category, and may even talk incessantly about racial conflict ... Whites discriminating against Blacks or Asians, for example.
All ethnic groups in America define themselves racially and we all participate in racial politics. Until that changes, attempts at dismissing the concept of race out of hand won't be particularly helpful.