"Redwood are algae" is a similar statement to "Pterodactyls are fish" or "bees are crustaceans". Redwoods are land plants, thus are also members of Viridiplantae - the clade containing land plants and green algae. The sister taxa to Viridiplantae in clade Archaeplastida are Glaucophyta (unicellular algae), and Rhodaria (contains red algae among other things). Thus since land plants are more closely related to green algae than green algae is to red algae or glaucophytes, if we want to treat the term "algae" as a monophyletic clade, then we have to include land plants in that, which of course includes redwoods. Essentially, this framing would make the term "algae" equivalent to Archaeplastida.

Another simpler interpretation (same idea as "ducks are dinosaurs") might be that all land plants evolved from algae, and nothing can evolve out of a clade, therefore plants must be algae. My hesitation to put this first is due to the fact that I'm unsure if the most recent common ancestor of green algae and plants would itself be classified as algae - this is an exercise left to the reader.