No, you just need to install ninja. It is a build tool like 'make'. You do not need ninja to run Chromium, just when compiling it.
The SlackBuild has these notes which you probably overlooked:
# Build needs: multilib gcc & glibc for compiling the Native Client (64-bit);
# libelf with '-D_FILE_OFFSET_BITS=64' added to CFLAGS (32-bit);