No, not when used properly.
DM has control over what inspiration encourages
The key thing here is that the DM controls when inspiration is awarded. As a DM, I give it freely and often and have never had a case of My Guy Syndrome (MGS) come specifically from this mechanic. In fact, I use it (successfully) as a way to reward players for non-MGS behaviors (behaviors the group as a whole find fun).
It could be used to create a worse problem though if you encourage the wrong things. In this case, you can make an MGS issue worse if you keep rewarding actions that are negatively affecting group fun in the name of good character RP. However, I think inspiration can only amplify a problem that already exists.
I sincerely doubt, and have never observed, that inspiration as a mechanic is powerful enough to actually cause MGS behaviors to appear outside of any other factors. And, on the flip side, when I have had problems with MGS at my table, inspiration has never been enough to fix it (and also runs afoul of my policy to fix out-of-game issues with out-of-game solutions as a first step).
My Guy Syndrome vs. Roleplaying
You seem to be conflating two things: role-playing and My Guy Syndrome. Role-playing often involves having a character have some sort of flaws or acting out drawbacks related to their personality or backstory. That's all part of storytelling. If every character was perfect and unflawed, stories about characters overcoming those flaws or developing as a character cease to exist. This is the kind of thing this passage is providing a mechanic to encourage.
On the other hand, My Guy Syndrome is what happens when you role-play any part of your character in a way that negatively affects your table's enjoyment and fun and then justify it as the only way you can act because it is what your character would do and that you have no choice but to do this.
If you are acting out a character flaw, and there is no issue with how much fun it is at the table and is not causing any other issues, then there is no problem and thus no MGS.
Other parts of the book provide more guidance that should be used with this
MGS is something that only occurs when a player is roleplaying as their character problematically. Anything that encourages more roleplaying without explicitly telling the player not to do so could be construed as "encouraging" MGS. However, the rules must be read in context. The portion that you read is in the DM's guidance for inspiration. In the PHB it says:
When another player character does something that really contributes to the story in a fun and interesting way, you can give up your inspiration to give that character inspiration.
Not the emphasis on group fun and story? That is pushing the players away from MGS. Taking one section of one part of the DM's manual without any of the other guidance the books offer on the matter is bound to give a skewed view of the guidance it offers. As with most things: context matters.