The reason that you know it is an emission spectrum, rather than an absorption spectrum, is that there are peaks rather than dips.
This is by definition: absorption lines are where light was absorbed by the atom, so you see a dip in the spectrum; emission lines are where the atom released a photon (whose energy corresponds to the energy difference of its quantum transition), so you see spikes/peaks in the spectrum.
Some spectra are complicated and can have both! For example, quasars can have emission spectra with "intervening" absorption lines due to either intervening interstellar gas in our galaxy or due to intergalactic gas along the line of sight to the quasar.
Wolf-Rayet stars are a complicated phenomenon. They are a class of stars that are broadly characterized as having little hydrogen in their spectra (i.e., the small emission line for H$\alpha$ in the OP's figure), and are dominated by strong emission lines corresponding to helium, nitrogen, carbon, and oxygen. The other trace elements in their spectra determine the type of WR star it is: nitrogen, carbon, or oxygen dominated, or some mixture.
Some Wolf-Rayet stars experience very intense stellar wind mass-loss, and hence are surrounded by a nebula of gas being expelled from the stellar surface. This nebula can cause absorption lines in Wolf-Rayet spectra, similar to the case of quasars. For example, WR 124.