Fraternal (brotherly) love is an essential aspect of the novella; there is no textual evidence that there is erotic love (even with regards to Curley's wife), or that Lennie even understands sexuality at all.
The novella isn't a love story in this sense, but the bond of love that George feels for Lennie is so strong that George would rather kill Lennie himself than subject him to torture (shooting in the gut by Curley) or confinement (in a "booby hatch" or asylum).
George's love for Lennie can be seen as parental in this context. It (of course) is similar to the love that Candy feels for his old dog.
Thematically, many of Steinbeck's characters must be cruel to be kind. Slim kills four puppies so that the other five may grow strong; Candy's dog must die because it lives in pain and no longer has any usefulness; and Lennie is killed to spare him agony.