TLDR: rules-as-written (RAW) means different things to different people. Here are some distinctions that I personally think make sense.
Rules-as-written, or RAW, as most people like to write it. What does it mean?
Used literally, it means whenever you have a question about how to play you follow what the rulebook says to the best of your ability. If you make a ruling at the table and a player looks it up then, or after the game, and finds a contradiction between your ruling and the text, you go with the text. It also means, in a literal sense, that you aren't subtracting, adding, or modifying the rules in any way.
It's pretty hard to play any game like that. There are bound to be some awkward and unclear phrasings, typos, or missing rules that make playing RAW difficult. The next step away is, I believe, rules-as-intended, RAI.
Rules-as-intended means that you stick close to the rules and play them as you believe they are supposed to be played. You are not adding, subtracting, or changing the rules unless there's clearly an error in the text, a rule is unplayable (wasn't play-tested), or you have to fill in a gap where the rules are silent. When you do fill in a gap, you do it by following the logic and spirit of the rules. You aren't inventing so much as extrapolating. Personally, I still consider this RAW, especially if the rules encourage you to invent/fill in the gaps.
Taking another step away from RAW is adding things that don't obviously change or interfere with existing rules, but clearly weren't intended by the original rules either. Let's call this Rules+. For instance, you bolt some kind of sanity mechanic onto Oe D&D. Or allow two-handed weapons to do more damage than other weapons to make up for the fact that their wielders are forgoing the use of a shield and may be attacking late in a round. The thing about adding rules is that no matter how careful you are, you are affecting existing mechanisms. Perhaps adding a Sanity mechanic makes the Intelligence ability score in D&D less important? Or adding a differentiation for two-handed weapons begs you to add rules for parallel instances, e.g. dual-wielded weapons, reach weapons, rate of fire, etc. Adding rules is a slippery slope, especially if what you liked about the original rules set was their "simplicity." Adding rules begets greater complexity.
Clearly, if there is a Rules+ there is a Rules–, meaning you drop some rules because they feel clunky, slow down play, aren't meaningful, etc. Subtracting may reduce complexity, but you may also be throwing out the baby with the bathwater. As with adding rules, you can quickly find yourself playing a different game. For example, the Save progressions are part of class strength and weaknesses, as well as a way to differentiate between the peril of various threat types, in Oe D&D. If you dump those in favor of straight roll-under tests by ability, you may be losing one of the classes' primary advantages (good Saves) or negating one of its drawbacks (bad Saves). Also, dropping Saves means dragon breath, poison, and rays are all roughly the same type of threat, aside from prescribed damage (and in Oe it's all d6 based).
Finally, there's hacking. It's hard to see where house-ruling ends and hacking begins sometimes. Changing the setting is a clue for a lot of observers, but you could very often change the setting of a game without touching its mechanisms, other than perhaps relabeling a few weapons. It's a distinction of quantity and quality. One big change or lots of little ones can result in the feeling that you are playing a different game. And the minute you feel like that, you have hacked the original. You have voided the warranty on play experience; if it goes south it's on you!
So, Are You Playing RAW?
It's my opinion that if you are doing literal RAW, RUI, or perhaps even light Rules+, you are. It's a matter of not believing you know more than the designer of the game and taking care to try the rules as written first before you make any adjustments or outright changes. Any such adjustments or changes should be governed by making the game play to its strengths, rather than making it feel different or fit a different style/genre of play. If that isn't your mindset, then you probably aren't playing RAW.