Here are some words that might help explain why some people feel there is a similarity. Emphasis added for...well, emphasis.
"Of the two approaches to hobby games today, one is best defined as the realism-simulation school and the other as the game school. [This game] is assuredly an adherent of the latter [game] school. It does not stress any realism (in the author's opinion an absurd effort at best considering the topic!). It does little to attempt to simulate anything either. [This game] is first and foremost a game for the fun* and enjoyment of those who seek to use imagination and creativity."
"In all cases ... the reader should understand that [this game] is designed to be an amusing and diverting pastime, something which can fill a few hours or consume endless days, as the participants desire, but in no case something to be taken too seriously. For fun*, excitement, and captivating fantasy, [this game] is unsurpassed. As a realistic simulation of things from the realm of make-believe, or even as a reflection of medieval or ancient warfare or culture or society, it can be deemed only a dismal failure. Readers who seek the latter must search elsewhere. Those who desire to create and populate imaginary worlds with larger-than-life heroes and villains, who seek relaxation with a fascinating game, and who generally believe games should be fun*, not work, will hopefully find this system to their taste."
These words were written by Gary Gygax about 1E. You can find them on page 9 of your 1E DMG.
*Good god, he used the word 'fun'! Three times!