I think there are really three conversations here:
1. Are various astral shard related mechanics (daily dice, chest rerolls) gambling?
Technically probably not, but they're not great. They are predatory mechanics that exploit dopamine cycles. Are they gacha game level bad? Not even close. That said, I also don't think they're actually pay to win- with the exception of some strong results from rolls (which are cheaper to just buy outright most of the time anyway) there isn't a lot on the daily dice to directly make you more powerful and rerolling chests is just getting more shots at the RNG.
2. If you spend money, do you get a better DDO experience beyond just accessing more content?
Absolutely. Tomes are the big one, and boosters are helpful to cut down on grind. That said, do you "win" if you spend money? Not automatically. I think there's a power difference between people who are maximized efficient whales and players who are maximized efficient F2P at any given time, but I don't think it's that big- the difference is how long it takes to get there. There are a handful of items at any given time you can't buy with points, and I wouldn't want to farm points to buy them as F2P, but it's mostly tomes which while powerful are not "win" level of powerful IMO.
3. Does spending money mean you can play the game and have fun while not spending money means you can't?
Yesn't. The free quest roster is a bit thin and I don't think you could meaningfully enjoy DDO for free. But pay to win and pay to play are two different categories just buying access to content, not power boosts, can make DDO a fun game. That's not pay to win, though, since it's about access, not instantly being more powerful.
All that to say, I think DDO is kind of in a weird position as far as MMOs go. I think, on the side of the free player experiences, DDO offers one of maybe the worst experiences in 2026 that you can find. It's introduction is dated and the free player experience has an extremely narrow slice of content and some unnecessary limits on features to push people towards VIP or at least premium account status. DDO's F2P experience is tragically bad, both in terms of content gates and QoL features gated behind premium status, a real legacy of it's early days when F2P MMOs were largely basically just demo versions of "real" MMOs, but with the ability to see everyone else with the cool stuff hidden behind the pay wall flaunting it in front of you.
That said, other than first time purchases content (which is a huge wall at the start of your DDO experience) DDO is actually relatively low "maintenance"- an annual VIP subscription and the standard edition of the yearly expansion will run you about $150, which if DDO is your primary gaming expense is not crazy high compared to something like World of Warcraft or FFXIV which can run that in just the base subscription to say nothing of their in game cash shops or one time purchases for content (and gacha games give that number a run for its money in a single banner). Sure, you can spend more than that if you really want to, but I think you're actually getting decent value for that and if you wait for sales for expansions you don't have you can save even more if you don't care about running the latest expansion.
From there you could spend money on powerups like tomes and boosts like potions, but I don't think it's necessary to play the game or have fun. I've played alts with no tomes and had a decent time of it, and I am far from the best DDO player. While I do have experience and shared storage to help me, I think a new player could enjoy DDO without any of that, especially if they know how to use the wiki. That has a pretty high ceiling but in my opinion it's pretty optional and even if you're interested in that, I'd recommend just waiting for sales unless you absolutely need that tome now for some reason.
So, yeah, I kind of got off topic but I think DDO is more "pay to play the game and then pay a bit more to have a better time while playing it", not really pay to win. There's a pretty big pay wall, which is a problem with DDO's current economy where new players are expected to cough up piles of cash for content that isn't really worth it anymore (or, at least, not looking through the eyes of a new player) or subscribe to VIP, which is a commitment for a 20 year old game. But the actual pay ceiling (outside of Otto's boxes and shards/boxes/pots) is pretty reasonable for an MMO of DDO's quality and scope, and I do legitimately think DDO is a much more interesting game to play than the competition.