You've explained it well, I only disagree with your last sentence. I think the chance of winning is absolutely the same either with martingale or betting with 1.1x multiplier. With this particular multiplier you have 10%+ chances of losing your whole balance right away, with the very first bet, even on a site with the smallest house edge.
You are right. I calculated the chance of winning in both cases.
Let's say I have 1 BTC and I want to convert it to 1.1 BTC.
If I put the whole 1 BTC is a single bet with multiplier of 1.1, my chance of winning would be 86.36%.
If I use martingale method and set the base bet to 0.001 mBTC, the chance of converting the 1 BTC to 1.1 BTC would be:
(1 - 0.525
10)
100 = 0.852 = 85.3%
That's why Martingale is sometimes known as "the extra house edge".
What Martingale is really meant for is allowing you to bet on outcomes that are less than the minimum bet odds. Your example shows a 1.1x and you could reduce that to 1.01x. But if you wanted to reduce it to 1.001x then Martingale is the only way you can do it.